Learning calculus from scratch
I have enrolled in a degree that requires maths involving calculus but i did not do mathematics B in high school, so i am looking for the best resources to reach a level that satisfies a high school maths b understanding.
What would be the best way to achieve this (book? online?...) Can anyone refer me to some online tutorials or books?
Would a wikibook be a worthy learning resource for these outcomes?
Calculus - Wikibooks, collection of open-content textbooks
The course has the following description and learning outcomes:
The course revises and extends basic integral and differential calculus of one variable, introduces partial derivatives and basic vector algebra in two and three dimensions. It provides a foundation for later studies in mathematics and science.
Prior Assumed: A grade of SA over 4 semesters in Mathematics B (Qld high school subject), or equivalent study over 4 semesters of a high school subject that includes the study of differential and integral calculus.
1 Manipulate 2D and 3D vectors and use vector addition and subtraction as well as the dot and
cross product of vectors. Use these ideas in problems involving geometric, force and velocity
2 Know and use the standard addition formulas for sin, cos and tan. To be able to prove some
of the simpler trig addition formulas To understand and use the inverse trigonometric functions.
3 Define and evaluate reasonably straightforward limits and be able to use and interpret the limit definition of the derivative.
4 Calculate derivatives using the sum, product, quotient and chain rule and to know the derivatives of the functions xn, ex, sin(x), cos(x), tan(x), loge(x), sin-1(x) and tan-1(x).
5 Identify the local maxima, minima and points of inflection of straightforward functions and use this information to sketch the graphs of these functions.
6 State and use the small change formula appropriately.
7 Convert word problems into mathematics and analyze these using calculus.
8 Be able to state and calculate Taylor approximations to standard functions.
9 Be able to state and use líHopitalís rule to evaluate 0/0 limits.
10 Understand the definition of integrals using Riemann sums and be able to provide a variety of situations in which the integral is used besides areas under curves.
11 Be able to state the Fundamental Theorem of Calculus and use anti-derivatives appropriately to evaluate definite and indefinite integrals.
12 Be able to use straightforward substitutions to evaluate integrals.
13 Use definite integrals to calculate areas, mean values and some related applications such as centroids, masses or straightforward volumes.
14 Understand the geometric meaning and the analytic definition of partial derivatives. be able to calculate the first and second derivatives of straightforward functions and be able to apply the small change formula for functions of several variables.