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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
Introduction
Convergence tests
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
Thomas, G. et al (2005). Thomas' Calculus:Early Transcendentals. 11th Edition: Pearson Education, Limited.
Stewart, J. Calculus Early Transcendentals. 8th edition. Belmont, CA: Brooks Cole.
Apostol, T. (1969). Calculus Vol. 1. 2D ED. John Wiley and Sons.
Spivak, M. (2006). Calculus. 4th Ed, Cambridge University Press.
