| Week 1 |
| Parametric Equations & Polar Coordinates: Parametric equations, polar coordinate system. Relationship between Cartesian and polar coordinates. |
| Week 2 |
| Graphs of polar equation and intersections point in polar coordinates. |
| Week 3 |
| Review: Graphs of trigonometric functions, exponential, trigonometric identities, and graphs of f and f –1 in general. Transcendental Functions: Hyperbolic functions, Inverse trigonometric functions, and inverse hyperbolic functions. |
| Week 4 |
| Graphs of hyperbolic, hyperbolic inverses and trigonometric inverses. Identities of hyperbolic and trigonometric inverses, and solving related equations |
| Week 5 |
| Differentiation (including implicit relation) of functions and relations involving hyperbolic and inverses. |
| Week 6 |
| Integration of functions involving hyperbolic and inverses using definition, identities and integration by parts. |
| Week 7 |
| Integration using substitution method, partial fraction, trigonometric and hyperbolic substitutions. |
| Week 8 |
| Further Applications of Integration: Arc length, area of surface of revolution in Cartesian form. |
| Week 9 |
| Arc length, area of surface of revolution in polar and parametric form. |
| Week 10 |
| Improper Integrals. L’Hopital’s Rule, Integral of first kind |
| Week 11 |
| Integral of second kind |
| Week 12 |
| Multivariable Functions: Terminology and notation, domain and range of two and three variables functions. Graphs of two variable functions: Surfaces and level curves. |
| Week 13 |
| Graphs of three variable functions: Level surfaces. |
| Week 14 |
| Limits and continuity: Notions of limits and continuity for functions of two variables including non-existence of limits (two paths rule). |
