Math 101 Chapter 4: Taylor series and complex numbers

• 4.2 Taylor series and complex numbers chapter contents
• 4.3 Polynomial approximation
• 4.4 Taylor’s polynomials
• 4.5 Differentiating Taylor polynomials
• 4.6 Taylor expansions
• 4.7 Maclaurin’s Theorem
• 4.8 The Maclaurin series for sine
• 4.9 Numerical values
• 4.10 The general binomial theorem
• 4.11 Binomial coefficients
• 4.12 Convergence of Taylor series.
• 4.13 Sign test for increasing or decreasing functions
• 4.14 Classification of stationary points
• 4.15 Number of stationary points
• 4.16 Sign test for stationary points
• 4.17 Proof of the sign test for stationary points
• 4.18 Cases of the sign test
• 4.19 Asymptotes
• 4.20 Systematic curve sketching
• 4.21 Stationary points
• 4.22 On using the sign tests
• 4.23 Limits of $x\log x$
• 4.24 $x\log x$
• 4.25 Summary (Remember these!)
• 4.26 Complex numbers
• 4.27 Argand’s diagram
• 4.28 Complex numbers
• 4.29 Arithmetic of complex numbers
• 4.30 Rules for addition and multiplication
• 4.31 Dividing complex numbers
• 4.32 Real quadratic equation
• 4.33 Complex trigonometric series
• 4.34 Complex exponentials and the unit circle
• 4.35 Polar form of complex numbers
• 4.36 Multiplying complex numbers in polar form
• 4.37 Geometrical interpretation of complex multiplication
• 4.38 De Moivre’s Theorem
• 4.39 Complex roots of unity
• 4.40 Simplifying multiple angles in terms of trig powers
• 4.41 Trig functions in terms of $z$
• 4.42 Expressing trig powers in terms of multiple angles
• 4.43 Principle of linear superposition
• 4.44 General solutions and initial conditions
• 4.45 Homogeneous second-order differential equation
• 4.46 Proof (i) Distinct real roots
• 4.47 Proof (ii) Double real root
• 4.48 Proof (iii) Complex conjugate roots
• 4.49 Complex solutions