Calculus 2

1. The Basics of Integration

� Antiderivatives

1. Antidifferentiation

2. Antiderivatives of Powers of x

3. Antiderivatives of Trigonometric and Exponential Functions

� Integration by Substitution

1. Undoing the Chain Rule

2. Integrating Polynomials by Substitution

� Illustrating Integration by Substitution

1. Integrating Composite Trigonometric Functions by Substitution

2. Integrating Composite Exponential and Rational Functions by Substitution

3. More Integrating Trigonometric Functions by Substitution

4. Choosing Effective Function Decompositions

� The Fundamental Theorem of Calculus

1. Approximating Areas of Plane Regions

2. Areas, Riemann Sums, and Definite Integrals

3. The Fundamental Theorem of Calculus

4. Illustrating the Fundamental Theorem of Calculus

5. Evaluating Definite Integrals

� Integration Using Tables

1. An Introduction to the Integral Table

� Numerical Integration

1. Deriving the Trapezoidal Rule

2. An Example of the Trapezoidal Rule

�

2. Applications of Integration

� Motion

1. Antiderivatives and Motion

2. Gravity and Vertical Motion

3. Solving Vertical Motion Problems

� Finding the Area between Two Curves

1. The Area between Two Curves

2. Limits of Integration and Area

3. Common Mistakes to Avoid When Finding Areas

4. Regions Bound by Several Curves

� Integrating with Respect to y

1. Finding Areas by Integrating with Respect to y: Part One

2. Finding Areas by Integrating with Respect to y: Part Two

3. Area, Integration by Substitution, and Trigonometry

� The Average Value of a Function

1. Finding the Average Value of a Function

� Finding Volumes Using Cross-Sections

1. Finding Volumes Using Cross-Sectional Slices

2. An Example of Finding Cross-Sectional Volumes

� Disks and Washers

1. Solids of Revolution

2. The Disk Method along the y-Axis

3. A Transcendental Example of the Disk Method

4. The Washer Method across the x-Axis

5. The Washer Method across the y-Axis

� Shells

1. Introducing the Shell Method

2. Why Shells Can Be Better Than Washers

3. The Shell Method: Integrating with Respect to y

� Work

1. An Introduction to Work��

2. Calculating Work

3. Hooke's Law

� Moments and Centers of Mass

1. Center of Mass

2. The Center of Mass of a Thin Plate

3. L'H�pital's Rule and Improper Integrals

� Indeterminate Quotients

1. Indeterminate Forms

2. An Introduction to L'H�pital's Rule

3. Basic Uses of L'H�pital's Rule

� Other Indeterminate Forms

1. L'H�pital's Rule and Indeterminate Products

2. L'H�pital's Rule and Indeterminate Differences

3. L'H�pital's Rule and One to the Infinite Power

� Improper Integrals

1. The First Type of Improper Integral

2. The Second Type of Improper Integral

3. Infinite Limits of Integration, Convergence, and Divergence



			Outline Page




	SUBJECT SYLLABUS




Mathematics

College Algebra Plane Geometry Solid Geometry Trigonometry Vector Analysis Calculus 1 Calculus 2 Physics 1 Physics 2 Physics 3 Physics 4 Statistics & Pobability Advance Math Numerical Analysis Mechanics Differential Equation Thermodynamics
		Calculus 1 Calculus 2 1. The Basics of Integration � Antiderivatives 1. Antidifferentiation 2. Antiderivatives of Powers of x 3. Antiderivatives of Trigonometric and Exponential Functions � Integration by Substitution 1. Undoing the Chain Rule 2. Integrating Polynomials by Substitution � Illustrating Integration by Substitution 1. Integrating Composite Trigonometric Functions by Substitution 2. Integrating Composite Exponential and Rational Functions by Substitution 3. More Integrating Trigonometric Functions by Substitution 4. Choosing Effective Function Decompositions � The Fundamental Theorem of Calculus 1. Approximating Areas of Plane Regions 2. Areas, Riemann Sums, and Definite Integrals 3. The Fundamental Theorem of Calculus 4. Illustrating the Fundamental Theorem of Calculus 5. Evaluating Definite Integrals � Integration Using Tables 1. An Introduction to the Integral Table � Numerical Integration 1. Deriving the Trapezoidal Rule 2. An Example of the Trapezoidal Rule � 2. Applications of Integration � Motion 1. Antiderivatives and Motion 2. Gravity and Vertical Motion 3. Solving Vertical Motion Problems � Finding the Area between Two Curves 1. The Area between Two Curves 2. Limits of Integration and Area 3. Common Mistakes to Avoid When Finding Areas 4. Regions Bound by Several Curves � Integrating with Respect to y 1. Finding Areas by Integrating with Respect to y: Part One 2. Finding Areas by Integrating with Respect to y: Part Two 3. Area, Integration by Substitution, and Trigonometry � The Average Value of a Function 1. Finding the Average Value of a Function � Finding Volumes Using Cross-Sections 1. Finding Volumes Using Cross-Sectional Slices 2. An Example of Finding Cross-Sectional Volumes � Disks and Washers 1. Solids of Revolution 2. The Disk Method along the y-Axis 3. A Transcendental Example of the Disk Method 4. The Washer Method across the x-Axis 5. The Washer Method across the y-Axis � Shells 1. Introducing the Shell Method 2. Why Shells Can Be Better Than Washers 3. The Shell Method: Integrating with Respect to y � Work 1. An Introduction to Work�� 2. Calculating Work 3. Hooke's Law � Moments and Centers of Mass 1. Center of Mass 2. The Center of Mass of a Thin Plate 3. L'H�pital's Rule and Improper Integrals � Indeterminate Quotients 1. Indeterminate Forms 2. An Introduction to L'H�pital's Rule 3. Basic Uses of L'H�pital's Rule � Other Indeterminate Forms 1. L'H�pital's Rule and Indeterminate Products 2. L'H�pital's Rule and Indeterminate Differences 3. L'H�pital's Rule and One to the Infinite Power � Improper Integrals 1. The First Type of Improper Integral 2. The Second Type of Improper Integral 3. Infinite Limits of Integration, Convergence, and Divergence Hosted by www.Geocities.ws