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Week 1 |
| Further Transcendental Functions: Inverse trigonometric functions, hyperbolic functions and its inverse in logarithmic form. Solving and proving equations related to these functions. |
Week 2 & 3 |
| Differentiation: Differentiation of functions involving inverse trigonometric functions, hyperbolic functions and inverse hyperbolic functions. Implicit and parametric differentiations. Chain rules and higher order differentiation. |
Week 4 & 5 |
| Integration: Integration techniques – standard integral table, substitution, by parts, and partial fractions. Integration of expressions involving inverse trigonometric functions, hyperbolic functions, inverse hyperbolic functions. Using table of integrals to integrate related functions. |
Week 6 |
| Improper Integrals: Evaluation of limits including L’Hopital rule, limits of indeterminate forms of type 0/0 and ∞/∞. Improper integrals with infinite limits of integration and infinite integrands. |
Week 7 |
| Series: Expansion of finite series, infinite series, and the summations of r, r2 and r3. Tests of convergence: divergence test, ratio test and integral test. Taylor’s series including Maclaurin’s series of standard functions including applications to find limits, and approximate definite integrals. Test 1 |
Week 8 |
| MID-SEMESTER BREAK |
Week 9 & 10 |
| Vectors: Vector in space and its operations including dot product and cross product. Equation of line and plane. Angle between two lines, intersection of two lines. Intersection of two planes. Shortest distance from a point to a line, a point to a plane. Angle between two planes, and angle between a line and a plane. |
Week 11 & 12 |
| Matrix Algebra: Minors, cofactors, adjoints, and determinants. Solve system of linear equations using inverse matrix and Cramer’s rule. Elementary row operations (ERO). Use ERO to obtain inverse matrix and solve system of linear equations using Gauss elimination. Involve cases like unique, many or no solution for system of linear equations. Eigenvalue and eigenvector. |
Week 13 |
| Polar Coordinates: Point representation in polar coordinates, relationship between polar and Cartesian coordinates. Graph sketching of polar equation including intersection between curves. Test 2 |
Week 14 & 15 |
| Complex Numbers: Definition of imaginary number and complex number. Algebraic operations and solving equations involving complex numbers. Modulus and argument. De Moivre’s theorem to show some trigonometric identities, to find power and roots of complex numbers. |
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