MA1S12: CALCULUS - BRIEF SUMMARY
1. The topics covered in Week 1 were:
(a) Integration by parts
(b) Tabular integration
(c) Reduction formulas
(d) Integrating products of trigonometric functions
These topics are covered in sections 7.2 and 7.3 of the calculus textbook.
2. The topics covered in Week 2 were:
(a) Trigonometric substitutions
(b) Computing area.
(c) Computing the length of a curve.
(d) Partial fractions
See sections 7.4, 5.1, 5.4 and 7.5 of the calculus book.
3. In Week 3 we covered:
(a) More partial fractions
(b) Computing the volume of a solid of revolution generated by
revolving about the x axis. (Method of disks)
(c) Improper integrals
See sections 7.5, 5.2 and 7.8 of the calculus book.
4. In Week 4 we covered the following topics:
(a) Numerical integration - midpoint, trapezoidal and Simpson’s
rule
(b) Computing the volume of a solid of revolution generated by
revolving about the y axis. (Method of cylindrical shells)
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MA1S12: CALCULUS - BRIEF SUMMARY
(c) Computing surface area of a surface of revolution generated by
revolving about the x-axis.
See sections 7.7, 5.3 and 5.5 of the Calculus textbook.
5. In Week 5 we covered the following topics:
(a) Solving first order separable ODE’s.
(b) Solving first order linear ODE’s.
(c) Generating a slope field for a first order ODE.
See sections 8.1, 8.2, 8.3, 8.4 of the Calculus textbook.
6. In Week 6 we covered the following topics:
(a) Euler’s method for approximating the solution to first order
ODE’s.
(b) Solving a second order ODE with application to position, velocity and acceleration.
(c) Exponential growth and decay models.
(d) Solving mixing problems with first order linear ODE’s.
See sections 8.1, 8.2, 8.3, 8.4 of the Calculus textbook.
7. Week 7 Reading week.
8. In Week 8 we covered the following topics:
(a) Sequences, computing limits, the Sandwich Theorem.
(b) Monotone Convergence Theorem, recursion formulae.
(c) Infinite series, convergence and divergence, geometric series.
See sections 9.1, 9.2, 9.3 of the Calculus textbook.
9. In Week 9 we covered the following topics:
(a) Convergence tests for infinite series: divergence test, ratio test,
integral test, p-series, limit comparison test.
(b) Comparison test, absolute convergence, root test.
(c) Power series, radius of convergence.
MA1S12: CALCULUS - BRIEF SUMMARY
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See sections 9.4, 9.5, 9.6 and 9.7 of the Calculus textbook.
10. In Week 10 we covered the following topics:
(a) Maclaurin and Taylor series.
(b) Applications of Taylor series: approximations, solving ODE’s,
integration.
See sections 9.8, 9.9, 9.10 of the Calculus textbook.
11. In Week 11 we covered the following topics:
(a) Parametric curves, computing length.
(b) Polar coordinates, polar curves.
(c) Computing tangent lines, length and area bounded by a polar
curve.
See sections 10.1, 10.2, 10.3 of the Calculus textbook.
12. In Week 12 we covered the following topics:
(a) Functions of several variables, graphs.
(b) Computing partial derivatives.
(c) Partial differential equations, Laplace and wave equation.
See sections 13.1, 13.3 of the Calculus textbook.