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AP Calculus AB Online Prep Course Prof. Raffi Hovasapian
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Level Advanced
66 Lessons (44hr : 00min)
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4.4 412 Ratings & 32 Reviews
Audio: English
English

Professor Raffi Hovasapian will help you ace the AP Calculus AB exam in this video prep series. Raffi takes complex math concepts and distills them into easy-to-understand fundamentals that are illustrated with numerous applications and sample problems. He also walks through an entire real Advanced Placement test while dispensing useful test-taking strategies that will help you get that 5.

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Course Details
About Prof. Hovasapian

Section 1: Limits and Derivatives
	Overview & Slopes of Curves			42:08
		Intro		0:00
		Overview & Slopes of Curves		0:21
			Differential and Integral	0:22
			Fundamental Theorem of Calculus	6:36
			Differentiation or Taking the Derivative	14:24
			What Does the Derivative Mean and How do We Find it?	15:18
			Example: f'(x)	19:24
			Example: f(x) = sin (x)	29:16
			General Procedure for Finding the Derivative of f(x)	37:33
	More on Slopes of Curves			50:53
		Intro		0:00
		Slope of the Secant Line along a Curve		0:12
			Slope of the Tangent Line to f(x) at a Particlar Point	0:13
			Slope of the Secant Line along a Curve	2:59
		Instantaneous Slope		6:51
			Instantaneous Slope	6:52
			Example: Distance, Time, Velocity	13:32
			Instantaneous Slope and Average Slope	25:42
		Slope & Rate of Change		29:55
			Slope & Rate of Change	29:56
			Example: Slope = 2	33:16
			Example: Slope = 4/3	34:32
			Example: Slope = 4 (m/s)	39:12
			Example: Density = Mass / Volume	40:33
			Average Slope, Average Rate of Change, Instantaneous Slope, and Instantaneous Rate of Change	47:46
	Example Problems for Slopes of Curves			59:12
		Intro		0:00
		Example I: Water Tank		0:13
			Part A: Which is the Independent Variable and Which is the Dependent?	2:00
			Part B: Average Slope	3:18
			Part C: Express These Slopes as Rates-of-Change	9:28
			Part D: Instantaneous Slope	14:54
		Example II: y = √(x-3)		28:26
			Part A: Calculate the Slope of the Secant Line	30:39
			Part B: Instantaneous Slope	41:26
			Part C: Equation for the Tangent Line	43:59
		Example III: Object in the Air		49:37
			Part A: Average Velocity	50:37
			Part B: Instantaneous Velocity	55:30
	Desmos Tutorial			18:43
		Intro		0:00
		Desmos Tutorial		1:42
			Desmos Tutorial	1:43
		Things You Must Learn To Do on Your Particular Calculator		2:39
			Things You Must Learn To Do on Your Particular Calculator	2:40
		Example I: y=sin x		4:54
		Example II: y=x³ and y = d/(dx) (x³)		9:22
		Example III: y = x² {-5 <= x <= 0} and y = cos x {0 < x < 6}		13:15
	The Limit of a Function			51:53
		Intro		0:00
		The Limit of a Function		0:14
			The Limit of a Function	0:15
			Graph: Limit of a Function	12:24
			Table of Values	16:02
			lim x→a f(x) Does not Say What Happens When x = a	20:05
		Example I: f(x) = x²		24:34
		Example II: f(x) = 7		27:05
		Example III: f(x) = 4.5		30:33
		Example IV: f(x) = 1/x		34:03
		Example V: f(x) = 1/x²		36:43
		The Limit of a Function, Cont.		38:16
			Infinity and Negative Infinity	38:17
			Does Not Exist	42:45
		Summary		46:48
	Example Problems for the Limit of a Function			24:43
		Intro		0:00
		Example I: Explain in Words What the Following Symbols Mean		0:10
		Example II: Find the Following Limit		5:21
		Example III: Use the Graph to Find the Following Limits		7:35
		Example IV: Use the Graph to Find the Following Limits		11:48
		Example V: Sketch the Graph of a Function that Satisfies the Following Properties		15:25
		Example VI: Find the Following Limit		18:44
		Example VII: Find the Following Limit		20:06
	Calculating Limits Mathematically			53:48
		Intro		0:00
		Plug-in Procedure		0:09
			Plug-in Procedure	0:10
		Limit Laws		9:14
			Limit Law 1	10:05
			Limit Law 2	10:54
			Limit Law 3	11:28
			Limit Law 4	11:54
			Limit Law 5	12:24
			Limit Law 6	13:14
			Limit Law 7	14:38
		Plug-in Procedure, Cont.		16:35
			Plug-in Procedure, Cont.	16:36
		Example I: Calculating Limits Mathematically		20:50
		Example II: Calculating Limits Mathematically		27:37
		Example III: Calculating Limits Mathematically		31:42
		Example IV: Calculating Limits Mathematically		35:36
		Example V: Calculating Limits Mathematically		40:58
		Limits Theorem		44:45
			Limits Theorem 1	44:46
			Limits Theorem 2: Squeeze Theorem	46:34
		Example VI: Calculating Limits Mathematically		49:26
	Example Problems for Calculating Limits Mathematically			21:22
		Intro		0:00
		Example I: Evaluate the Following Limit by Showing Each Application of a Limit Law		0:16
		Example II: Evaluate the Following Limit		1:51
		Example III: Evaluate the Following Limit		3:36
		Example IV: Evaluate the Following Limit		8:56
		Example V: Evaluate the Following Limit		11:19
		Example VI: Calculating Limits Mathematically		13:19
		Example VII: Calculating Limits Mathematically		14:59
	Calculating Limits as x Goes to Infinity			50:01
		Intro		0:00
		Limit as x Goes to Infinity		0:14
			Limit as x Goes to Infinity	0:15
			Let's Look at f(x) = 1 / (x-3)	1:04
			Summary	9:34
		Example I: Calculating Limits as x Goes to Infinity		12:16
		Example II: Calculating Limits as x Goes to Infinity		21:22
		Example III: Calculating Limits as x Goes to Infinity		24:10
		Example IV: Calculating Limits as x Goes to Infinity		36:00
	Example Problems for Limits at Infinity			36:31
		Intro		0:00
		Example I: Calculating Limits as x Goes to Infinity		0:14
		Example II: Calculating Limits as x Goes to Infinity		3:27
		Example III: Calculating Limits as x Goes to Infinity		8:11
		Example IV: Calculating Limits as x Goes to Infinity		14:20
		Example V: Calculating Limits as x Goes to Infinity		20:07
		Example VI: Calculating Limits as x Goes to Infinity		23:36
	Continuity			53:00
		Intro		0:00
		Definition of Continuity		0:08
			Definition of Continuity	0:09
			Example: Not Continuous	3:52
			Example: Continuous	4:58
			Example: Not Continuous	5:52
			Procedure for Finding Continuity	9:45
		Law of Continuity		13:44
			Law of Continuity	13:45
		Example I: Determining Continuity on a Graph		15:55
		Example II: Show Continuity & Determine the Interval Over Which the Function is Continuous		17:57
		Example III: Is the Following Function Continuous at the Given Point?		22:42
		Theorem for Composite Functions		25:28
			Theorem for Composite Functions	25:29
		Example IV: Is cos(x³ + ln x) Continuous at x=π/2?		27:00
		Example V: What Value of A Will make the Following Function Continuous at Every Point of Its Domain?		34:04
		Types of Discontinuity		39:18
			Removable Discontinuity	39:33
			Jump Discontinuity	40:06
			Infinite Discontinuity	40:32
		Intermediate Value Theorem		40:58
			Intermediate Value Theorem: Hypothesis & Conclusion	40:59
			Intermediate Value Theorem: Graphically	43:40
		Example VI: Prove That the Following Function Has at Least One Real Root in the Interval [4,6]		47:46
	Derivative I			40:02
		Intro		0:00
		Derivative		0:09
			Derivative	0:10
		Example I: Find the Derivative of f(x)=x³		2:20
		Notations for the Derivative		7:32
			Notations for the Derivative	7:33
		Derivative & Rate of Change		11:14
			Recall the Rate of Change	11:15
			Instantaneous Rate of Change	17:04
			Graphing f(x) and f'(x)	19:10
		Example II: Find the Derivative of x⁴ - x²		24:00
		Example III: Find the Derivative of f(x)=√x		30:51
	Derivatives II			53:45
		Intro		0:00
		Example I: Find the Derivative of (2+x)/(3-x)		0:18
		Derivatives II		9:02
			f(x) is Differentiable if f'(x) Exists	9:03
			Recall: For a Limit to Exist, Both Left Hand and Right Hand Limits Must Equal to Each Other	17:19
			Geometrically: Differentiability Means the Graph is Smooth	18:44
		Example II: Show Analytically that f(x) = \|x\| is Nor Differentiable at x=0		20:53
			Example II: For x > 0	23:53
			Example II: For x < 0	25:36
			Example II: What is f(0) and What is the lim \|x\| as x→0?	30:46
		Differentiability & Continuity		34:22
			Differentiability & Continuity	34:23
		How Can a Function Not be Differentiable at a Point?		39:38
			How Can a Function Not be Differentiable at a Point?	39:39
		Higher Derivatives		41:58
			Higher Derivatives	41:59
			Derivative Operator	45:12
		Example III: Find (dy)/(dx) & (d²y)/(dx²) for y = x³		49:29
	More Example Problems for The Derivative			31:38
		Intro		0:00
		Example I: Sketch f'(x)		0:10
		Example II: Sketch f'(x)		2:14
		Example III: Find the Derivative of the Following Function sing the Definition		3:49
		Example IV: Determine f, f', and f'' on a Graph		12:43
		Example V: Find an Equation for the Tangent Line to the Graph of the Following Function at the Given x-value		13:40
		Example VI: Distance vs. Time		20:15
		Example VII: Displacement, Velocity, and Acceleration		23:56
		Example VIII: Graph the Displacement Function		28:20
Section 2: Differentiation
	Differentiation of Polynomials & Exponential Functions			47:35
		Intro		0:00
		Differentiation of Polynomials & Exponential Functions		0:15
			Derivative of a Function	0:16
			Derivative of a Constant	2:35
			Power Rule	3:08
			If C is a Constant	4:19
			Sum Rule	5:22
			Exponential Functions	6:26
		Example I: Differentiate		7:45
		Example II: Differentiate		12:38
		Example III: Differentiate		15:13
		Example IV: Differentiate		16:20
		Example V: Differentiate		19:19
		Example VI: Find the Equation of the Tangent Line to a Function at a Given Point		12:18
		Example VII: Find the First & Second Derivatives		25:59
		Example VIII		27:47
			Part A: Find the Velocity & Acceleration Functions as Functions of t	27:48
			Part B: Find the Acceleration after 3 Seconds	30:12
			Part C: Find the Acceleration when the Velocity is 0	30:53
			Part D: Graph the Position, Velocity, & Acceleration Graphs	32:50
		Example IX: Find a Cubic Function Whose Graph has Horizontal Tangents		34:53
		Example X: Find a Point on a Graph		42:31
	The Product, Power & Quotient Rules			47:25
		Intro		0:00
		The Product, Power and Quotient Rules		0:19
			Differentiate Functions	0:20
			Product Rule	5:30
			Quotient Rule	9:15
			Power Rule	10:00
		Example I: Product Rule		13:48
		Example II: Quotient Rule		16:13
		Example III: Power Rule		18:28
		Example IV: Find dy/dx		19:57
		Example V: Find dy/dx		24:53
		Example VI: Find dy/dx		28:38
		Example VII: Find an Equation for the Tangent to the Curve		34:54
		Example VIII: Find d²y/dx²		38:08
	Derivatives of the Trigonometric Functions			41:08
		Intro		0:00
		Derivatives of the Trigonometric Functions		0:09
			Let's Find the Derivative of f(x) = sin x	0:10
			Important Limits to Know	4:59
			d/dx (sin x)	6:06
			d/dx (cos x)	6:38
			d/dx (tan x)	6:50
			d/dx (csc x)	7:02
			d/dx (sec x)	7:15
			d/dx (cot x)	7:27
		Example I: Differentiate f(x) = x² - 4 cos x		7:56
		Example II: Differentiate f(x) = x⁵ tan x		9:04
		Example III: Differentiate f(x) = (cos x) / (3 + sin x)		10:56
		Example IV: Differentiate f(x) = e^x / (tan x - sec x)		14:06
		Example V: Differentiate f(x) = (csc x - 4) / (cot x)		15:37
		Example VI: Find an Equation of the Tangent Line		21:48
		Example VII: For What Values of x Does the Graph of the Function x + 3 cos x Have a Horizontal Tangent?		25:17
		Example VIII: Ladder Problem		28:23
		Example IX: Evaluate		33:22
		Example X: Evaluate		36:38
	The Chain Rule			24:56
		Intro		0:00
		The Chain Rule		0:13
			Recall the Composite Functions	0:14
			Derivatives of Composite Functions	1:34
		Example I: Identify f(x) and g(x) and Differentiate		6:41
		Example II: Identify f(x) and g(x) and Differentiate		9:47
		Example III: Differentiate		11:03
		Example IV: Differentiate f(x) = -5 / (x² + 3)³		12:15
		Example V: Differentiate f(x) = cos(x² + c²)		14:35
		Example VI: Differentiate f(x) = cos⁴x +c²		15:41
		Example VII: Differentiate		17:03
		Example VIII: Differentiate f(x) = sin(tan x²)		19:01
		Example IX: Differentiate f(x) = sin(tan² x)		21:02
		Example X: Differentiate f(x) = (x²-2)⁴ (5x² - 2x -2)⁸
	More Chain Rule Example Problems			25:32
		Intro		0:00
		Example I: Differentiate f(x) = sin(cos(tanx))		0:38
		Example II: Find an Equation for the Line Tangent to the Given Curve at the Given Point		2:25
		Example III: F(x) = f(g(x)), Find F' (6)		4:22
		Example IV: Differentiate & Graph both the Function & the Derivative in the Same Window		5:35
		Example V: Differentiate f(x) = ( (x-8)/(x+3) )⁴		10:18
		Example VI: Differentiate f(x) = sec²(12x)		12:28
		Example VII: Differentiate		14:41
		Example VIII: Differentiate		19:25
		Example IX: Find an Expression for the Rate of Change of the Volume of the Balloon with Respect to Time		21:13
	Implicit Differentiation			52:31
		Intro		0:00
		Implicit Differentiation		0:09
			Implicit Differentiation	0:10
		Example I: Find (dy)/(dx) by both Implicit Differentiation and Solving Explicitly for y		12:15
		Example II: Find (dy)/(dx) of x³ + x²y + 7y² = 14		19:18
		Example III: Find (dy)/(dx) of x³y² + y³x² = 4x		21:43
		Example IV: Find (dy)/(dx) of the Following Equation		24:13
		Example V: Find (dy)/(dx) of 6sin x cos y = 1		29:00
		Example VI: Find (dy)/(dx) of x² cos² y + y sin x = 2sin x cos y		31:02
		Example VII: Find (dy)/(dx) of √(xy) = 7 + y²e^x		37:36
		Example VIII: Find (dy)/(dx) of 4(x²+y²)² = 35(x²-y²)		41:03
		Example IX: Find (d²y)/(dx²) of x² + y² = 25		44:05
		Example X: Find (d²y)/(dx²) of sin x + cos y = sin(2x)		47:48
Section 3: Applications of the Derivative
	Linear Approximations & Differentials			47:34
		Intro		0:00
		Linear Approximations & Differentials		0:09
			Linear Approximations & Differentials	0:10
		Example I: Linear Approximations & Differentials		11:27
		Example II: Linear Approximations & Differentials		20:19
		Differentials		30:32
			Differentials	30:33
		Example III: Linear Approximations & Differentials		34:09
		Example IV: Linear Approximations & Differentials		35:57
		Example V: Relative Error		38:46
	Related Rates			45:33
		Intro		0:00
		Related Rates		0:08
			Strategy for Solving Related Rates Problems #1	0:09
			Strategy for Solving Related Rates Problems #2	1:46
			Strategy for Solving Related Rates Problems #3	2:06
			Strategy for Solving Related Rates Problems #4	2:50
			Strategy for Solving Related Rates Problems #5	3:38
		Example I: Radius of a Balloon		5:15
		Example II: Ladder		12:52
		Example III: Water Tank		19:08
		Example IV: Distance between Two Cars		29:27
		Example V: Line-of-Sight		36:20
	More Related Rates Examples			37:17
		Intro		0:00
		Example I: Shadow		0:14
		Example II: Particle		4:45
		Example III: Water Level		10:28
		Example IV: Clock		20:47
		Example V: Distance between a House and a Plane		29:11
	Maximum & Minimum Values of a Function			40:44
		Intro		0:00
		Maximum & Minimum Values of a Function, Part 1		0:23
			Absolute Maximum	2:20
			Absolute Minimum	2:52
			Local Maximum	3:38
			Local Minimum	4:26
		Maximum & Minimum Values of a Function, Part 2		6:11
			Function with Absolute Minimum but No Absolute Max, Local Max, and Local Min	7:18
			Function with Local Max & Min but No Absolute Max & Min	8:48
		Formal Definitions		10:43
			Absolute Maximum	11:18
			Absolute Minimum	12:57
			Local Maximum	14:37
			Local Minimum	16:25
			Extreme Value Theorem	18:08
			Theorem: f'(c) = 0	24:40
			Critical Number (Critical Value)	26:14
			Procedure for Finding the Critical Values of f(x)	28:32
		Example I: Find the Critical Values of f(x) x + sinx		29:51
		Example II: What are the Absolute Max & Absolute Minimum of f(x) = x + 4 sinx on [0,2π]		35:31
	Example Problems for Max & Min			40:44
		Intro		0:00
		Example I: Identify Absolute and Local Max & Min on the Following Graph		0:11
		Example II: Sketch the Graph of a Continuous Function		3:11
		Example III: Sketch the Following Graphs		4:40
		Example IV: Find the Critical Values of f (x) = 3x⁴ - 7x³ + 4x²		6:13
		Example V: Find the Critical Values of f(x) = \|2x - 5\|		8:42
		Example VI: Find the Critical Values		11:42
		Example VII: Find the Critical Values f(x) = cos²(2x) on [0,2π]		16:57
		Example VIII: Find the Absolute Max & Min f(x) = 2sinx + 2cos x on [0,(π/3)]		20:08
		Example IX: Find the Absolute Max & Min f(x) = (ln(2x)) / x on [1,3]		24:39
	The Mean Value Theorem			25:54
		Intro		0:00
		Rolle's Theorem		0:08
			Rolle's Theorem: If & Then	0:09
			Rolle's Theorem: Geometrically	2:06
			There May Be More than 1 c Such That f'( c ) = 0	3:30
		Example I: Rolle's Theorem		4:58
		The Mean Value Theorem		9:12
			The Mean Value Theorem: If & Then	9:13
			The Mean Value Theorem: Geometrically	11:07
		Example II: Mean Value Theorem		13:43
		Example III: Mean Value Theorem		21:19
	Using Derivatives to Graph Functions, Part I			25:54
		Intro		0:00
		Using Derivatives to Graph Functions, Part I		0:12
			Increasing/ Decreasing Test	0:13
		Example I: Find the Intervals Over Which the Function is Increasing & Decreasing		3:26
		Example II: Find the Local Maxima & Minima of the Function		19:18
		Example III: Find the Local Maxima & Minima of the Function		31:39
	Using Derivatives to Graph Functions, Part II			44:58
		Intro		0:00
		Using Derivatives to Graph Functions, Part II		0:13
			Concave Up & Concave Down	0:14
			What Does This Mean in Terms of the Derivative?	6:14
			Point of Inflection	8:52
		Example I: Graph the Function		13:18
		Example II: Function x⁴ - 5x²		19:03
			Intervals of Increase & Decrease	19:04
			Local Maxes and Mins	25:01
			Intervals of Concavity & X-Values for the Points of Inflection	29:18
			Intervals of Concavity & Y-Values for the Points of Inflection	34:18
			Graphing the Function	40:52
	Example Problems I			49:19
		Intro		0:00
		Example I: Intervals, Local Maxes & Mins		0:26
		Example II: Intervals, Local Maxes & Mins		5:05
		Example III: Intervals, Local Maxes & Mins, and Inflection Points		13:40
		Example IV: Intervals, Local Maxes & Mins, Inflection Points, and Intervals of Concavity		23:02
		Example V: Intervals, Local Maxes & Mins, Inflection Points, and Intervals of Concavity		34:36
	Example Problems III			59:01
		Intro		0:00
		Example I: Intervals, Local Maxes & Mins, Inflection Points, Intervals of Concavity, and Asymptotes		0:11
		Example II: Intervals, Local Maxes & Mins, Inflection Points, Intervals of Concavity, and Asymptotes		21:24
		Example III: Cubic Equation f(x) = Ax³ + Bx² + Cx + D		37:56
		Example IV: Intervals, Local Maxes & Mins, Inflection Points, Intervals of Concavity, and Asymptotes		46:19
	L'Hospital's Rule			30:09
		Intro		0:00
		L'Hospital's Rule		0:19
			Indeterminate Forms	0:20
			L'Hospital's Rule	3:38
		Example I: Evaluate the Following Limit Using L'Hospital's Rule		8:50
		Example II: Evaluate the Following Limit Using L'Hospital's Rule		10:30
		Indeterminate Products		11:54
			Indeterminate Products	11:55
		Example III: L'Hospital's Rule & Indeterminate Products		13:57
		Indeterminate Differences		17:00
			Indeterminate Differences	17:01
		Example IV: L'Hospital's Rule & Indeterminate Differences		18:57
		Indeterminate Powers		22:20
			Indeterminate Powers	22:21
		Example V: L'Hospital's Rule & Indeterminate Powers		25:13
	Example Problems for L'Hospital's Rule			38:14
		Intro		0:00
		Example I: Evaluate the Following Limit		0:17
		Example II: Evaluate the Following Limit		2:45
		Example III: Evaluate the Following Limit		6:54
		Example IV: Evaluate the Following Limit		8:43
		Example V: Evaluate the Following Limit		11:01
		Example VI: Evaluate the Following Limit		14:48
		Example VII: Evaluate the Following Limit		17:49
		Example VIII: Evaluate the Following Limit		20:37
		Example IX: Evaluate the Following Limit		25:16
		Example X: Evaluate the Following Limit		32:44
	Optimization Problems I			49:59
		Intro		0:00
		Example I: Find the Dimensions of the Box that Gives the Greatest Volume		1:23
		Fundamentals of Optimization Problems		18:08
			Fundamental #1	18:33
			Fundamental #2	19:09
			Fundamental #3	19:19
			Fundamental #4	20:59
			Fundamental #5	21:55
			Fundamental #6	23:44
		Example II: Demonstrate that of All Rectangles with a Given Perimeter, the One with the Largest Area is a Square		24:36
		Example III: Find the Points on the Ellipse 9x² + y² = 9 Farthest Away from the Point (1,0)		35:13
		Example IV: Find the Dimensions of the Rectangle of Largest Area that can be Inscribed in a Circle of Given Radius R		43:10
	Optimization Problems II			55:10
		Intro		0:00
		Example I: Optimization Problem		0:13
		Example II: Optimization Problem		17:34
		Example III: Optimization Problem		35:06
		Example IV: Revenue, Cost, and Profit		43:22
	Newton's Method			30:22
		Intro		0:00
		Newton's Method		0:45
			Newton's Method	0:46
		Example I: Find x2 and x3		13:18
		Example II: Use Newton's Method to Approximate		15:48
		Example III: Find the Root of the Following Equation to 6 Decimal Places		19:57
		Example IV: Use Newton's Method to Find the Coordinates of the Inflection Point		23:11
Section 4: Integrals
	Antiderivatives			55:26
		Intro		0:00
		Antiderivatives		0:23
			Definition of an Antiderivative	0:24
			Antiderivative Theorem	7:58
		Function & Antiderivative		12:10
			x^n	12:30
			1/x	13:00
			e^x	13:08
			cos x	13:18
			sin x	14:01
			sec² x	14:11
			secxtanx	14:18
			1/√(1-x²)	14:26
			1/(1+x²)	14:36
			-1/√(1-x²)	14:45
		Example I: Find the Most General Antiderivative for the Following Functions		15:07
			Function 1: f(x) = x³ -6x² + 11x - 9	15:42
			Function 2: f(x) = 14√(x) - 27 4√x	19:12
			Function 3: (fx) = cos x - 14 sinx	20:53
			Function 4: f(x) = (x⁵+2√x )/( x^(4/3) )	22:10
			Function 5: f(x) = (3e^x) - 2/(1+x²)	25:42
		Example II: Given the Following, Find the Original Function f(x)		26:37
			Function 1: f'(x) = 5x³ - 14x + 24, f(2) = 40	27:55
			Function 2: f'(x) 3 sinx + sec²x, f(π/6) = 5	30:34
			Function 3: f''(x) = 8x - cos x, f(1.5) = 12.7, f'(1.5) = 4.2	32:54
			Function 4: f''(x) = 5/(√x), f(2) 15, f'(2) = 7	37:54
		Example III: Falling Object		41:58
			Problem 1: Find an Equation for the Height of the Ball after t Seconds	42:48
			Problem 2: How Long Will It Take for the Ball to Strike the Ground?	48:30
			Problem 3: What is the Velocity of the Ball as it Hits the Ground?	49:52
			Problem 4: Initial Velocity of 6 m/s, How Long Does It Take to Reach the Ground?	50:46
	The Area Under a Curve			51:03
		Intro		0:00
		The Area Under a Curve		0:13
			Approximate Using Rectangles	0:14
			Let's Do This Again, Using 4 Different Rectangles	9:40
		Approximate with Rectangles		16:10
			Left Endpoint	18:08
			Right Endpoint	25:34
			Left Endpoint vs. Right Endpoint	30:58
			Number of Rectangles	34:08
		True Area		37:36
			True Area	37:37
			Sigma Notation & Limits	43:32
			When You Have to Explicitly Solve Something	47:56
	Example Problems for Area Under a Curve			33:07
		Intro		0:00
		Example I: Using Left Endpoint & Right Endpoint to Approximate Area Under a Curve		0:10
		Example II: Using 5 Rectangles, Approximate the Area Under the Curve		11:32
		Example III: Find the True Area by Evaluating the Limit Expression		16:07
		Example IV: Find the True Area by Evaluating the Limit Expression		24:52
	The Definite Integral			43:19
		Intro		0:00
		The Definite Integral		0:08
			Definition to Find the Area of a Curve	0:09
			Definition of the Definite Integral	4:08
			Symbol for Definite Integral	8:45
			Regions Below the x-axis	15:18
			Associating Definite Integral to a Function	19:38
			Integrable Function	27:20
		Evaluating the Definite Integral		29:26
			Evaluating the Definite Integral	29:27
		Properties of the Definite Integral		35:24
			Properties of the Definite Integral	35:25
	Example Problems for The Definite Integral			32:14
		Intro		0:00
		Example I: Approximate the Following Definite Integral Using Midpoints & Sub-intervals		0:11
		Example II: Express the Following Limit as a Definite Integral		5:28
		Example III: Evaluate the Following Definite Integral Using the Definition		6:28
		Example IV: Evaluate the Following Integral Using the Definition		17:06
		Example V: Evaluate the Following Definite Integral by Using Areas		25:41
		Example VI: Definite Integral		30:36
	The Fundamental Theorem of Calculus			24:17
		Intro		0:00
		The Fundamental Theorem of Calculus		0:17
			Evaluating an Integral	0:18
			Lim as x → ∞	12:19
			Taking the Derivative	14:06
			Differentiation & Integration are Inverse Processes	15:04
		1st Fundamental Theorem of Calculus		20:08
			1st Fundamental Theorem of Calculus	20:09
		2nd Fundamental Theorem of Calculus		22:30
			2nd Fundamental Theorem of Calculus	22:31
	Example Problems for the Fundamental Theorem			25:21
		Intro		0:00
		Example I: Find the Derivative of the Following Function		0:17
		Example II: Find the Derivative of the Following Function		1:40
		Example III: Find the Derivative of the Following Function		2:32
		Example IV: Find the Derivative of the Following Function		5:55
		Example V: Evaluate the Following Integral		7:13
		Example VI: Evaluate the Following Integral		9:46
		Example VII: Evaluate the Following Integral		12:49
		Example VIII: Evaluate the Following Integral		13:53
		Example IX: Evaluate the Following Graph		15:24
			Local Maxs and Mins for g(x)	15:25
			Where Does g(x) Achieve Its Absolute Max on [0,8]	20:54
			On What Intervals is g(x) Concave Up/Down?	22:20
			Sketch a Graph of g(x)	24:34
	More Example Problems, Including Net Change Applications			34:22
		Intro		0:00
		Example I: Evaluate the Following Indefinite Integral		0:10
		Example II: Evaluate the Following Definite Integral		0:59
		Example III: Evaluate the Following Integral		2:59
		Example IV: Velocity Function		7:46
			Part A: Net Displacement	7:47
			Part B: Total Distance Travelled	13:15
		Example V: Linear Density Function		20:56
		Example VI: Acceleration Function		25:10
			Part A: Velocity Function at Time t	25:11
			Part B: Total Distance Travelled During the Time Interval	28:38
	Solving Integrals by Substitution			27:20
		Intro		0:00
		Table of Integrals		0:35
		Example I: Evaluate the Following Indefinite Integral		2:02
		Example II: Evaluate the Following Indefinite Integral		7:27
		Example IIII: Evaluate the Following Indefinite Integral		10:57
		Example IV: Evaluate the Following Indefinite Integral		12:33
		Example V: Evaluate the Following		14:28
		Example VI: Evaluate the Following		16:00
		Example VII: Evaluate the Following		19:01
		Example VIII: Evaluate the Following		21:49
		Example IX: Evaluate the Following		24:34
Section 5: Applications of Integration
	Areas Between Curves			34:56
		Intro		0:00
		Areas Between Two Curves: Function of x		0:08
			Graph 1: Area Between f(x) & g(x)	0:09
			Graph 2: Area Between f(x) & g(x)	4:07
			Is It Possible to Write as a Single Integral?	8:20
			Area Between the Curves on [a,b]	9:24
			Absolute Value	10:32
			Formula for Areas Between Two Curves: Top Function - Bottom Function	17:03
		Areas Between Curves: Function of y		17:49
			What if We are Given Functions of y?	17:50
			Formula for Areas Between Two Curves: Right Function - Left Function	21:48
			Finding a & b	22:32
	Example Problems for Areas Between Curves			42:55
		Intro		0:00
		Instructions for the Example Problems		0:10
		Example I: y = 7x - x² and y=x		0:37
		Example II: x=y²-3, x=e^((1/2)y), y=-1, and y=2		6:25
		Example III: y=(1/x), y=(1/x³), and x=4		12:25
		Example IV: 15-2x² and y=x²-5		15:52
		Example V: x=(1/8)y³ and x=6-y²		20:20
		Example VI: y=cos x, y=sin(2x), [0,π/2]		24:34
		Example VII: y=2x², y=10x², 7x+2y=10		29:51
		Example VIII: Velocity vs. Time		33:23
			Part A: At 2.187 Minutes, Which care is Further Ahead?	33:24
			Part B: If We Shaded the Region between the Graphs from t=0 to t=2.187, What Would This Shaded Area Represent?	36:32
			Part C: At 4 Minutes Which Car is Ahead?	37:11
			Part D: At What Time Will the Cars be Side by Side?	37:50
	Volumes I: Slices			34:15
		Intro		0:00
		Volumes I: Slices		0:18
			Rotate the Graph of y=√x about the x-axis	0:19
			How can I use Integration to Find the Volume?	3:16
			Slice the Solid Like a Loaf of Bread	5:06
			Volumes Definition	8:56
		Example I: Find the Volume of the Solid Obtained by Rotating the Region Bounded by the Given Functions about the Given Line of Rotation		12:18
		Example II: Find the Volume of the Solid Obtained by Rotating the Region Bounded by the Given Functions about the Given Line of Rotation		19:05
		Example III: Find the Volume of the Solid Obtained by Rotating the Region Bounded by the Given Functions about the Given Line of Rotation		25:28
	Volumes II: Volumes by Washers			51:43
		Intro		0:00
		Volumes II: Volumes by Washers		0:11
			Rotating Region Bounded by y=x³ & y=x around the x-axis	0:12
			Equation for Volumes by Washer	11:14
			Process for Solving Volumes by Washer	13:40
		Example I: Find the Volume of the Solid Obtained by Rotating the Region Bounded by the Following Functions around the Given Axis		15:58
		Example II: Find the Volume of the Solid Obtained by Rotating the Region Bounded by the Following Functions around the Given Axis		25:07
		Example III: Find the Volume of the Solid Obtained by Rotating the Region Bounded by the Following Functions around the Given Axis		34:20
		Example IV: Find the Volume of the Solid Obtained by Rotating the Region Bounded by the Following Functions around the Given Axis		44:05
	Volumes III: Solids That Are Not Solids-of-Revolution			49:36
		Intro		0:00
		Solids That Are Not Solids-of-Revolution		0:11
			Cross-Section Area Review	0:12
			Cross-Sections That Are Not Solids-of-Revolution	7:36
		Example I: Find the Volume of a Pyramid Whose Base is a Square of Side-length S, and Whose Height is H		10:54
		Example II: Find the Volume of a Solid Whose Cross-sectional Areas Perpendicular to the Base are Equilateral Triangles		20:39
		Example III: Find the Volume of a Pyramid Whose Base is an Equilateral Triangle of Side-Length A, and Whose Height is H		29:27
		Example IV: Find the Volume of a Solid Whose Base is Given by the Equation 16x² + 4y² = 64		36:47
		Example V: Find the Volume of a Solid Whose Base is the Region Bounded by the Functions y=3-x² and the x-axis		46:13
	Volumes IV: Volumes By Cylindrical Shells			50:02
		Intro		0:00
		Volumes by Cylindrical Shells		0:11
			Find the Volume of the Following Region	0:12
			Volumes by Cylindrical Shells: Integrating Along x	14:12
			Volumes by Cylindrical Shells: Integrating Along y	14:40
			Volumes by Cylindrical Shells Formulas	16:22
		Example I: Using the Method of Cylindrical Shells, Find the Volume of the Solid		18:33
		Example II: Using the Method of Cylindrical Shells, Find the Volume of the Solid		25:57
		Example III: Using the Method of Cylindrical Shells, Find the Volume of the Solid		31:38
		Example IV: Using the Method of Cylindrical Shells, Find the Volume of the Solid		38:44
		Example V: Using the Method of Cylindrical Shells, Find the Volume of the Solid		44:03
	The Average Value of a Function			32:13
		Intro		0:00
		The Average Value of a Function		0:07
			Average Value of f(x)	0:08
			What if The Domain of f(x) is Not Finite?	2:23
			Let's Calculate Average Value for f(x) = x² [2,5]	4:46
			Mean Value Theorem for Integrate	9:25
		Example I: Find the Average Value of the Given Function Over the Given Interval		14:06
		Example II: Find the Average Value of the Given Function Over the Given Interval		18:25
		Example III: Find the Number A Such that the Average Value of the Function f(x) = -4x² + 8x + 4 Equals 2 Over the Interval [-1,A]		24:04
		Example IV: Find the Average Density of a Rod		27:47
Section 6: Techniques of Integration
	Integration by Parts			50:32
		Intro		0:00
		Integration by Parts		0:08
			The Product Rule for Differentiation	0:09
			Integrating Both Sides Retains the Equality	0:52
			Differential Notation	2:24
		Example I: ∫ x cos x dx		5:41
		Example II: ∫ x² sin(2x)dx		12:01
		Example III: ∫ (e^x) cos x dx		18:19
		Example IV: ∫ (sin^-1) (x) dx		23:42
		Example V: ∫₁⁵ (lnx)² dx		28:25
		Summary		32:31
		Tabular Integration		35:08
			Case 1	35:52
			Example: ∫x³sinx dx	36:39
			Case 2	40:28
			Example: ∫e^(2x) sin 3x	41:14
	Trigonometric Integrals I			24:50
		Intro		0:00
		Example I: ∫ sin³ (x) dx		1:36
		Example II: ∫ cos⁵(x)sin²(x)dx		4:36
		Example III: ∫ sin⁴(x)dx		9:23
		Summary for Evaluating Trigonometric Integrals of the Following Type: ∫ (sin^m) (x) (cos^p) (x) dx		15:59
			#1: Power of sin is Odd	16:00
			#2: Power of cos is Odd	16:41
			#3: Powers of Both sin and cos are Odd	16:55
			#4: Powers of Both sin and cos are Even	17:10
		Example IV: ∫ tan⁴ (x) sec⁴ (x) dx		17:34
		Example V: ∫ sec⁹(x) tan³(x) dx		20:55
		Summary for Evaluating Trigonometric Integrals of the Following Type: ∫ (sec^m) (x) (tan^p) (x) dx		23:31
			#1: Power of sec is Odd	23:32
			#2: Power of tan is Odd	24:04
			#3: Powers of sec is Odd and/or Power of tan is Even	24:18
	Trigonometric Integrals II			22:12
		Intro		0:00
		Trigonometric Integrals II		0:09
			Recall: ∫tanx dx	0:10
			Let's Find ∫secx dx	3:23
		Example I: ∫ tan⁵ (x) dx		6:23
		Example II: ∫ sec⁵ (x) dx		11:41
		Summary: How to Deal with Integrals of Different Types		19:04
			Identities to Deal with Integrals of Different Types	19:05
		Example III: ∫cos(5x)sin(9x)dx		19:57
	More Example Problems for Trigonometric Integrals			17:22
		Intro		0:00
		Example I: ∫sin²(x)cos⁷(x)dx		0:14
		Example II: ∫x sin²(x) dx		3:56
		Example III: ∫csc⁴ (x/5)dx		8:39
		Example IV: ∫( (1-tan²x)/(sec²x) ) dx		11:17
		Example V: ∫ 1 / (sinx-1) dx		13:19
	Integration by Partial Fractions I			55:12
		Intro		0:00
		Integration by Partial Fractions I		0:11
			Recall the Idea of Finding a Common Denominator	0:12
			Decomposing a Rational Function to Its Partial Fractions	4:10
			2 Types of Rational Function: Improper & Proper	5:16
		Improper Rational Function		7:26
			Improper Rational Function	7:27
		Proper Rational Function		11:16
			Proper Rational Function & Partial Fractions	11:17
			Linear Factors	14:04
			Irreducible Quadratic Factors	15:02
		Case 1: G(x) is a Product of Distinct Linear Factors		17:10
		Example I: Integration by Partial Fractions		20:33
		Case 2: D(x) is a Product of Linear Factors		40:58
		Example II: Integration by Partial Fractions		44:41
	Integration by Partial Fractions II			42:57
		Intro		0:00
		Case 3: D(x) Contains Irreducible Factors		0:09
		Example I: Integration by Partial Fractions		5:19
		Example II: Integration by Partial Fractions		16:22
		Case 4: D(x) has Repeated Irreducible Quadratic Factors		27:30
		Example III: Integration by Partial Fractions		30:19
Section 7: Differential Equations
	Introduction to Differential Equations			46:37
		Intro		0:00
		Introduction to Differential Equations		0:09
			Overview	0:10
			Differential Equations Involving Derivatives of y(x)	2:08
			Differential Equations Involving Derivatives of y(x) and Function of y(x)	3:23
			Equations for an Unknown Number	6:28
			What are These Differential Equations Saying?	10:30
		Verifying that a Function is a Solution of the Differential Equation		13:00
			Verifying that a Function is a Solution of the Differential Equation	13:01
			Verify that y(x) = 4e^x + 3x² + 6x + e^π is a Solution of this Differential Equation	17:20
			General Solution	22:00
			Particular Solution	24:36
			Initial Value Problem	27:42
		Example I: Verify that a Family of Functions is a Solution of the Differential Equation		32:24
		Example II: For What Values of K Does the Function Satisfy the Differential Equation		36:07
		Example III: Verify the Solution and Solve the Initial Value Problem		39:47
	Separation of Variables			28:08
		Intro		0:00
		Separation of Variables		0:28
			Separation of Variables	0:29
		Example I: Solve the Following g Initial Value Problem		8:29
		Example II: Solve the Following g Initial Value Problem		13:46
		Example III: Find an Equation of the Curve		18:48
	Population Growth: The Standard & Logistic Equations			51:07
		Intro		0:00
		Standard Growth Model		0:30
			Definition of the Standard/Natural Growth Model	0:31
			Initial Conditions	8:00
			The General Solution	9:16
		Example I: Standard Growth Model		10:45
		Logistic Growth Model		18:33
			Logistic Growth Model	18:34
			Solving the Initial Value Problem	25:21
			What Happens When t → ∞	36:42
		Example II: Solve the Following g Initial Value Problem		41:50
		Relative Growth Rate		46:56
			Relative Growth Rate	46:57
			Relative Growth Rate Version for the Standard model	49:04
	Slope Fields			24:37
		Intro		0:00
		Slope Fields		0:35
			Slope Fields	0:36
			Graphing the Slope Fields, Part 1	11:12
			Graphing the Slope Fields, Part 2	15:37
			Graphing the Slope Fields, Part 3	17:25
		Steps to Solving Slope Field Problems		20:24
		Example I: Draw or Generate the Slope Field of the Differential Equation y'=x cos y		22:38
Section 8: AP Practic Exam
	AP Practice Exam: Section 1, Part A No Calculator			45:29
		Intro		0:00
		Exam Link		0:10
		Problem #1		1:26
		Problem #2		2:52
		Problem #3		4:42
		Problem #4		7:03
		Problem #5		10:01
		Problem #6		13:49
		Problem #7		15:16
		Problem #8		19:06
		Problem #9		23:10
		Problem #10		28:10
		Problem #11		31:30
		Problem #12		33:53
		Problem #13		37:45
		Problem #14		41:17
	AP Practice Exam: Section 1, Part A No Calculator, cont.			41:55
		Intro		0:00
		Problem #15		0:22
		Problem #16		3:10
		Problem #17		5:30
		Problem #18		8:03
		Problem #19		9:53
		Problem #20		14:51
		Problem #21		17:30
		Problem #22		22:12
		Problem #23		25:48
		Problem #24		29:57
		Problem #25		33:35
		Problem #26		35:57
		Problem #27		37:57
		Problem #28		40:04
	AP Practice Exam: Section I, Part B Calculator Allowed			58:47
		Intro		0:00
		Problem #1		1:22
		Problem #2		4:55
		Problem #3		10:49
		Problem #4		13:05
		Problem #5		14:54
		Problem #6		17:25
		Problem #7		18:39
		Problem #8		20:27
		Problem #9		26:48
		Problem #10		28:23
		Problem #11		34:03
		Problem #12		36:25
		Problem #13		39:52
		Problem #14		43:12
		Problem #15		47:18
		Problem #16		50:41
		Problem #17		56:38
	AP Practice Exam: Section II, Part A Calculator Allowed			25:40
		Intro		0:00
		Problem #1: Part A		1:14
		Problem #1: Part B		4:46
		Problem #1: Part C		8:00
		Problem #2: Part A		12:24
		Problem #2: Part B		16:51
		Problem #2: Part C		17:17
		Problem #3: Part A		18:16
		Problem #3: Part B		19:54
		Problem #3: Part C		21:44
		Problem #3: Part D		22:57
	AP Practice Exam: Section II, Part B No Calculator			31:20
		Intro		0:00
		Problem #4: Part A		1:35
		Problem #4: Part B		5:54
		Problem #4: Part C		8:50
		Problem #4: Part D		9:40
		Problem #5: Part A		11:26
		Problem #5: Part B		13:11
		Problem #5: Part C		15:07
		Problem #5: Part D		19:57
		Problem #6: Part A		22:01
		Problem #6: Part B		25:34
		Problem #6: Part C		28:54

Duration: 44 hours, 00 minutes

Number of Lessons: 66

This online course is crucial for students who want to score well on their AP Calculus AB exam. Although geared towards high school students taking the Calculus AB course and exam, this course is also indispensible for college students in the first semester of Calculus. Each topic begins with Raffi breaking down a concept into easily understood steps, followed by tons of examples that help cement learning. The course ends with a walkthrough of a real full-length AP test complete with useful strategies and tips.

Additional Features:

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Downloadable Lecture Slides
Instructor Comments

Topics Include:

Slopes of Curves
Continuity
Derivatives
Product, Power, & Quotient Rule
Chain Rule
Related Rates
Maximum & Minimum Values
Mean Value Theorem
L'Hospital's Rule
Antiderivatives

With his 15+ years teaching and tutoring experience coupled with triple majors in Chemistry, Mathematics, and Classics, Raffi's gift is explaining difficult concepts in simple-to-understand terms. Be sure to check out his other beloved math & science courses on Educator!

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4.4

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By Roy Jiang•January 3, 2019

Hello Professor Raffi,

I was just wondering if it was any coincidence that in example V, if I took Pi*30.4^2 - Pi*29.6^2 and divided the answer, I would get the possible error in area? And is this a valid way to approach a question like example V?

Thank you,

RJ

By Magic Fu•July 7, 2018

Thank You so much!!!!
My textbook sucks, it has zero practice problems and examples.
Lucky, I found your AP Calc AB videos, and I got 5 on my Calc BC and Calc AB exams.

(Also, I took AP Chemistry exam last year, but I ended up with a 4, which I am still very salty about that).

By Patricia Xiang•April 28, 2018

Thank you professor, I have got the refund!

By Patricia Xiang•April 19, 2018

Hello professor,

Is Reduced Echelon form required in AP calculus? Or it is just helpful solving the problems? And if it helps a lot, should I acquire how to do it by hands or merely how to do it on the calculator?

Have a great day.

By Tewodros Belachew•December 17, 2017

Ohh okay, I got it! Thank you