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4.0

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1 MB|300 pages

Product Description

Calculus Study Guide suitable for AP Calculus or First Year College Calculus Students. Main topics covered : Functions Limits and Continuity, Derivatives, Application of the Derivative, Indefinite integration, Definite Integration, Techniques of Integration, Sequences and Series, L’Hopitals Rule, Improper Integrals, Taylor Series, Short Introduction to Differential Equations.

Calculus without Limits is a self-study guide that can be used as a textbook/lecture supplement by students, as a source of homework problems by the instructor or as a source of lecture material. Covers most topics discussed in a first year calculus course (or AP Calculus). The emphasis is on solved problems that show students how to attack the types of problems they will encounter in homework and on exams. Discussion of concepts is informal followed by example problems. Many practice problems are also included for students.

1 - Function Review

What is a function - Graphing - Even and Odd Functions - Increasing and Decreasing Functions - One to One Functions - Powers and Polynomials - Absolute Value Function - Exponential Function - Logarithm - Trigonometric Functions

2- Limits

Definition - Tricks for Doing Limits - Properties of Limits and Rules - Limits at Infinity - One Sided Limits Continuity

3- Derivative

Notation and Definition in terms of limits - Slope of Tangent Line - Power Rule and Derivative of a constant - Chain Rule - Derivatives of Trig Functions - Product and Quotient Rules

4- Applications of the Derivative

Derivative of Inverse Function - Implicit Differentiation - Application: Rates of Change, Velocity and Acceleration - Finding Minima and Maxima First and Second Derivative Test - Inflection Points - The Mean Value Theorem - Related Rates

5- The Integral

Notation - Power Rule of Integration - Integration of Trig Functions - Integration of inverse function - Integrating Exponential Function - The substitution technique - Integrating Hyperbolic Functions - Definite Integration - Sums and Area Under a Curve - Area Between Two Curves -

6- U-Substitution

Solved Problems

7- Integration by Parts

Definition and When to Use - Examples

8- Integration of Rational Functions

Introduction - Examples

9- Integration Using the Method of Partial Fractions

Discussion - Examples

10- Integrating Powers of Trig Functions

Examples

11- Trig Substitution

Three Cases - Basic Technique -Examples

12 - Improper Integrals

Definition - Examples

13 - Sequences and Infinite Series

Sequences - Limits - Infinite Series

14 Ratio, Comparison, and Integral Tests

Examples

15 - Alternating Series

16 - Power Series and Radius of Convergence

17- Taylor Series Expansions

18- L’Hopital’s Rule

When to use and Definition - Examples

19- Introduction to Differential Equations

First Order Differential Equations - Second Order Differential Equations

Calculus without Limits is a self-study guide that can be used as a textbook/lecture supplement by students, as a source of homework problems by the instructor or as a source of lecture material. Covers most topics discussed in a first year calculus course (or AP Calculus). The emphasis is on solved problems that show students how to attack the types of problems they will encounter in homework and on exams. Discussion of concepts is informal followed by example problems. Many practice problems are also included for students.

1 - Function Review

What is a function - Graphing - Even and Odd Functions - Increasing and Decreasing Functions - One to One Functions - Powers and Polynomials - Absolute Value Function - Exponential Function - Logarithm - Trigonometric Functions

2- Limits

Definition - Tricks for Doing Limits - Properties of Limits and Rules - Limits at Infinity - One Sided Limits Continuity

3- Derivative

Notation and Definition in terms of limits - Slope of Tangent Line - Power Rule and Derivative of a constant - Chain Rule - Derivatives of Trig Functions - Product and Quotient Rules

4- Applications of the Derivative

Derivative of Inverse Function - Implicit Differentiation - Application: Rates of Change, Velocity and Acceleration - Finding Minima and Maxima First and Second Derivative Test - Inflection Points - The Mean Value Theorem - Related Rates

5- The Integral

Notation - Power Rule of Integration - Integration of Trig Functions - Integration of inverse function - Integrating Exponential Function - The substitution technique - Integrating Hyperbolic Functions - Definite Integration - Sums and Area Under a Curve - Area Between Two Curves -

6- U-Substitution

Solved Problems

7- Integration by Parts

Definition and When to Use - Examples

8- Integration of Rational Functions

Introduction - Examples

9- Integration Using the Method of Partial Fractions

Discussion - Examples

10- Integrating Powers of Trig Functions

Examples

11- Trig Substitution

Three Cases - Basic Technique -Examples

12 - Improper Integrals

Definition - Examples

13 - Sequences and Infinite Series

Sequences - Limits - Infinite Series

14 Ratio, Comparison, and Integral Tests

Examples

15 - Alternating Series

16 - Power Series and Radius of Convergence

17- Taylor Series Expansions

18- L’Hopital’s Rule

When to use and Definition - Examples

19- Introduction to Differential Equations

First Order Differential Equations - Second Order Differential Equations

Total Pages

300 pages

Answer Key

N/A

Teaching Duration

1 Year

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