| Resource | Description | / |
|---|---|---|
| George Thomas Jr, Maurice Weir, and Joel Hass, Thomas’ Calculus Early Transcendentals, 2008, 13th Edition, Pearson, ISBN-13: 978-1292021232 | / | |
| Week | Topic | Chapters |
| 1 | Limit of a Function & Limit Laws Meaning of Function Limit. Graphical Representation of the Limit of a Function. Existence of Limits of a Function. The Limit Laws. The Sandwich Theorem. | 1 |
| 2 | One-Sided Limits Approaching Limit from One-Side. Meaning of One-Sided Limit. The sin(x)/x case. Intermediate Value Theorem. | 2 |
| 3 | Continuity Concept of Continuity of a Function. Continuous Function. Limit of Continuous Function & Extension of a Point. Extension of a Function | 3 |
| 4 | Limits involving Infinity; Asymptotes of Graphs Finite Limits as ‘x’ approaches Infinity. Horizontal Asymptotes. Vertical Asymptotes. Infinite Limits. | 4 |
| 5 | The Derivatives as a Function Slope, Lines and Tangent Lines. Tangents and Derivatives. Derivative of a Function using Definition. Other Notation and Higher Derivatives. | 5 |
| 6 | Derivatives of Trigonometric Functions, The Chain Rule Differentiation Formula for Special Functions. Rules of Differentiation. Review of Trigonometric Functions. Derivative of Basic Trigonometric Functions. Derivative of Functions involving Trigonometric Functions. | 6 |
| 7 | Implicit Differentiation Differentiation of Problems involving both ‘x’ and ‘y’. | 7 |
| 8 | Derivatives of Inverse Functions and Logarithms, Inverse Trigonometric Functions Inverse Functions Logarithms. Derivative of Inverse Functions. Logarithmic Differentiation. Derivative of Basic Inverse Trigonometric Functions. Derivative of Functions that involve Inverse Trigonometric Functions. | 8 |
| 9 | Related Rates, Linearisation and Differentials Derivative as Rate of Change. Related Rates. Linear Approximation. | 9 |
| 10 | Midterm Revision Sessions | 1-9 |
| 11 | Anti-Derivatives Calculation of Anti-Derivatives of a Function. Word Problems involving Physics/ Real-Life Scenarios. | 10 |
| 12 | The Definite Integral, The Fundamental Theorem of Calculus Definition of the Integral. Difference between Differentiation and Integration. Properties of Integral. Differentiation and Integration as Inverse Processes. | 11 |
| 13 | Indefinite Integrals, The Substitution Method Difference between Definite & Indefinite Integrals. Integration by Substitution Method. | 12 |
| 14 | Substitution and Area Between Curves, Extreme Values of Functions Determination of Maximum & Minimum Values of a Function. Local Minima/ Maxima. Global Minima/ Maxima. The Extreme Value Theorem. | 13 |
| 15 | Monotonic Functions & 1st Derivative Test, Concavity & Curve Sketching Definition of Monotonic Function. Increasing & Decreasing Function. Concave-Upward, Concave-Downward & No-Curvature of Slope of a Function. Curve Sketching of a Function. | 14 |
| 16 | Applied Optimisation Problems on Optimisation of Area, Perimeter by Function Values Optimisation. | 15 |
| 17 | Final Exam Revision Sessions | 10-15 |