Ahmedghoor

Combined all the summaries of the content that I had created from the Test scopes we were given. Therefore these summaries focus on testable content, instead of all the useless "nice-to-know" stuff. That said, it is not entirely complete.

Summarised most of STA1006S content

Differential Equations, Vectors, Matrices and Linear Transformations

The test will cover material from everything that wasn't covered in test 1 up to what was covered by the end of last term (excluding related rates), which corresponds to the coming week's homework. The detailed breakdown of it is as follows: • Inverse functions, logs and inverse trig functions (parts of Stewart 6.1,6.3 and 6.6) • Proof by contradiction (Resource book) • Proof by induction (Resource book) • The limit of a function (Stewart 1.5) • Calculating limits using the limi...

Here is a list of the topics that we will be testing: • Related Rates (Stewart 2.8) • Maximum and Minimum Values (Stewart 3.1) • The Mean Value Theorem (Stewart 3.2) • How derivatives affect the shape of graphs (Stewart 3.3) • Curve sketching (Stewart 3.5) • L'hospital's rule (Stewart 6.8) • Optimization problems (Stewart 3.7) Proofs that you are expected to know • Rolle's Theorem (proof in the Mathematics Resource Book as well as in Stewart) • The Mean Value Theor...

Topics for test 4: • Antiderivatives - Stewart 3.9 • Sigma notation - Stewart Appendix E • Areas and distances- Stewart 4.1 • The definite integral - Stewart 4.2 • The Fundamental Theorem of Calculus - Stewart 4.3 • Indefinite integrals and the net change theorem - Stewart 4.4 • The substitution rule - Stewart 4.5 • Integration by parts - Stewart 7.1 • Trigonometric integrals - Stewart 7.2 • Trigonometric substitution - Stewart 7.3 • Partial fractions - Stewart 7...

The topics for test 5 are • Factorials - Resource book 2 • 1-1 functions and permutations - Resource book 2 • Falling factorials - Resource book 2 • Combinations - Resource book 2 • Binomial coefficients and Pascal’s Triangle - Resource book 2 • The Binomial Theorem - Resource book 2 • Maclaurin and Taylor polynomials - Stewart 11.10 (polynomials, and not series). • Elementary properties of complex numbers (all complex numbers sections are taken from the resource book)...