What are you going to learn?

Content

Evaluate indefinite and definite integrals, involving logarithmic and exponential functions. Solve problems involving Mean – Value Theorem and the Fundamental Theorem of Calculus. Evaluate integrals by different methods of integration. Differentiate between different types of indeterminate forms and finding limit of functions. Test improper integrals for convergence. Calculate areas of plane regions and arc length. Calculate volumes by both washers and cylindrical shells methods. Calculate areas of plane regions and arc length using polar coordinates.

Chapter 1. Definite Integrals

• Introduction

• Area Under the Curve

• Sigma Notation

• The Definite Integral

• The Mean Value Theorem

• The Fundamental Theorem of Calculus

• Area of a Region in a Plane

• Volumen of a Solid of Revolution

• Work

• Liquid Pressure

• Center of Mass

• Length of Arc of a Plane Curve

• Anti-derivatives

Chapter 2. Applications of Definite Integral

Chapter 3. Integrals and Transcendental Functions

• The Logarithm Defined as an Integral

• Exponential Functions

• Hyperbolic Functions

Chapter 4. techniques of Integration

• Basic Formulas

• Integration by Parts

• Trigonometric Integrals

• Trigonometric Substitutions

• Integration of Rational Functions by Partial Fractions

• Numerical Integration with Python

Chapter 5. Improper Integrals

• Infinite Limits of Integration

• Integrands with Vertical Asymptotes

• Improper Integrals with Python

• Tests for Convergence and Divergence

• Preventive Actions

Chapter 6. First Order Differential Equations

• Solutions, Slopes, and Euler’s Method

• First Order Linear Equations

• Applications

• Systems of Equations and Phase Planes

Chapter 7. Infinite Sequences and Series

1. Introduction

2. Convergence tests

3. Alternating series

Chapter 8. Power Series

• Sequences

• Infinite Series

• Integral Test

• Comparison Test

• Absolute Convergence: The Ratio and Root Tests

• Alternating Series and Conditional Convergence

• The Binomial Series

Bibliography

1. Thomas, G. et al (2005). Thomas’ Calculus:Early Transcendentals. 11th Edition: Pearson Education, Limited.

2. Stewart, J. Calculus Early Transcendentals. 8th edition. Belmont, CA: Brooks Cole.

3. Apostol, T. (1969). Calculus Vol. 1. 2D ED. John Wiley and Sons.

4. Spivak, M. (2006). Calculus. 4th Ed, Cambridge University Press.

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