Calculus II Module Syllabus
| Resource | Description | / |
|---|---|---|
| Required Book | Anton, H., Bivens, I. & Davis, S. (2012) Calculus 10th Edition – John Wiley & Sons, Inc. | / |
| Recommended Reading | Bird, J. (2021) Bird’s Higher Engineering Mathematics 9th Edition – Routledge Taylor & Francis Group | / |
| Other Resources | Online sources and journals YouTube tutorials | / |
| Week | Topic | Chapters on Book |
| Introductory Sessions | Introduction to the Course Explanation of course content & syllabus Recap on Fundamental Algebra Concepts Review on Basic Algebra Rules Definition of a Function and its Variables Graphs of Functions Geometric Effects on the Graphs of Functions Inverse Functions Operations on Functions Review on Differentiation | Chapter 0 |
| 1 | TRANSCENDENTAL FUNCTIONS Introduction to Transcendental Functions Main Classifications of Functions Algebraic Functions Definition of Transcendental Functions Types of Transcendental Functions Trigonometric Functions and their Inverses Basic Definitions of Trigonometric Functions Graphs of Trigonometric Functions Trigonometric Identities Derivatives of Trigonometric Functions Inverse Trigonometric Functions Derivatives of Inverse Trigonometric Functions | Chapter 6 |
| 2 | Hyperbolic Functions and their Inverses Basic Definitions of Hyperbolic Functions Graphs of Hyperbolic Functions Hyperbolic Identities Derivatives of Hyperbolic Functions Inverse Hyperbolic Functions Derivatives of Inverse Hyperbolic Functions Exponential and Logarithmic Functions Basic Definitions of Exponential Functions Basic Definitions of Logarithmic Functions Natural Exponential Function Natural Logarithmic Function Properties of Exponential and Logarithmic Functions Relationship Between Exponential and Logarithmic Functions Derivatives of Exponential and Logarithmic Functions | Chapter 6 |
| 3 | Applications of Transcendental Functions L’Hopital’s Rule Recap on Limits Types of Indeterminate Forms | Chapter 6 |
| 4 | INTEGRATION Introduction to Integration Area Problem Indefinite Integrals Definite Integrals Fundamental Theorem of Calculus | Chapters 4,5,6 & 7 |
| 5 | Methods of Integration Standard Integration Formulas Integration by Substitution Integration by Parts Integration by Partial Fractions Integration by Trigonometric Substitution Numerical Integration Improper Integrals | Chapters 4,5,6 & 7 |
| 8-9 | Midterm Revision Sessions | |
| 10-12 | Applications of Integration Rectilinear Motion Average Value of a Function Area Between Two Curves Volume of a Solid of Revolution Volumes by Cylindrical Shells Length of a Plane Curve Area of a Surface of Revolution Work Moments, Centers of Gravity, and Centroids Fluid Pressure and Force | Chapters 4 & 5 |
| 13 | Sequences Basic Theory on Sequences Monotonicity Infinite Series Sums of Infinite Series Geometric Series Harmonic Series | Chapter 9 |
| 14 | Properties and Tests on Infinite Series Divergence Test Algebraic Properties of Infinite Series Integral Test Comparison Test Ratio Test Root Test Alternating Series Sums of Alternating Series Convergence of Alternating Series | Chapter 9 |
| 15 | Maclaurin and Taylor Polynomials Maclaurin and Taylor Series: Power Series Convergence of Taylor Series Differentiation and Integration of Power Series | Chapter 9 |
| 16 | Final Exam Revision Sessions | |