Everything you Should Have Learned in Calculus

In my time as a Physics major I’ve noticed that the calculus 1-3 courses are often insufficient in preparing majors for the mathematics of middle to upper division physics classes. To help remedy this, I’ve decided to make a reference jupyter book of useful math from calculus 1-3 that comes up in physics courses. This is not expansive, and does not cover nearly every subject from these courses. This is more like a “greatest hits” album of calculus, and is meant only for reference.

What isn’t here

I’ve left out differential equations and (for the most part) linear algebra from this in the interest of not making this project too long. Perhaps in the future I will write on these subjects.

Table of contents:

Calc 1

• Notation
• Real Numbers
• Limits and Continuity
• Derivatives
• Function Palooza

Calc 2

• Differentiation vs Integration
• Geometric (and other) Series
• Taylor Series
• Change of Variables
• Symbolic Integration Methods

Calc 3

• Differentials of Functions of Multiple Variables
• Vectors and Vector Spaces
• Multi-Dimensional Operators
• Line Integrals
• Surface Integrals and Orientation
• Green’s Theorem
• Stokes’ Theorem
• Gauss’ Theorem

Further Topics

• Fourier Series
• The Stirling Approximation of N!
• The Dirac Delta “Function”
• The Heavyside Step Function
• Gaussians
• Calculus with Complex-Valued Functions
• Minkowsky Inequality