Math 101 Chapter 2: Functions of a real variable

• 2.2 Functions of a real variable chapter contents
• 2.3 Functions
• 2.4 Functions, Domains and Codomains
• 2.5 Real functions
• 2.6 Graphs and Continuity
• 2.7 Parabolas
• 2.8 Continuous and discontinuous graphs
• 2.9 Discontinuous real functions
• 2.10 A function diverging at a point
• 2.11 Tends to
• 2.12 Continuity and limits
• 2.13 Limits
• 2.14 Example
• 2.15 Continuity and limits
• 2.16 The modulus functions
• 2.17 Curve Sketching
• 2.18 Euler’s number e
• 2.19 The exponential function $\exp x$ or $e^{x}$
• 2.20 Properties of the exponential.
• 2.21 Proof of power law
• 2.22 Exponential growth
• 2.23 Graphs of the exponential functions
• 2.24 Hyperbolic functions
• 2.25 Hyperbolic identities
• 2.26 The reciprocal hyperbolic functions
• 2.27 Exponential series
• 2.28 Standard limits of functions
• 2.29 Nonsensical limits
• 2.30 Composite function
• 2.31 Inverse functions
• 2.32 Graphs of inverse functions
• 2.33 The inverse sine function $\sin^{-1}$ or arcsin
• 2.34 The log function $\log$ or $\ln$
• 2.35 Properties of log
• 2.36 Proofs of the properties of logs
• 2.37 Powers $a^{x}$
• 2.38 Power laws
• 2.39 Appendix: Trigonometric functions
• 2.40 Appendix: Basic right-angled triangle
• 2.41 Appendix: The reciprocal trigonometric functions
• 2.42 Appendix: Trigonometric addition rules
• 2.43 Appendix: Double-angle formulae