Calculus
If you do not understand your existing textbook then this is an excellent book to start reading.
Contents- Rates of Change: Change in discrete steps, Two sides of the same coin, Some guesses
- Continuous change: A derivative, Properties of the derivative, Higher-order polynomials, The second derivative, Maxima and minima
- Infinity and beyond! Infinitesimals, Safe use of infinitesimals, The product rule, The chain rule, Exponentials and logarithms, The exponential, The logarithm, Quotients, Differentiation on a computer, Continuity, Limits, L’H opital’s rule, Another perspective on indeterminate forms.
- Integration: Definite and indefinite integrals, The fundamental theorem of calculus, Properties of the integral, Applications, Averages, Work, Probability.
- Techniques: Newton’s method, Implicit differentiation, Taylor series, Methods of integration, Change of variable, Integration by parts, Partial fractions
- Complex number techniques: Review of complex numbers, Euler’s formula, Partial fractions revisited.
- Improper integrals: Integrating a function that blows up, Limits of integration at infinity.
- Iterated integrals: Integrals inside integrals, Applications, Polar coordinates, Spherical and cylindrical coordinates
