# CALCULUS:  Class Notes

Prof.  G. Battaly, Westchester Community College, Valhalla NY  (updated 01/10/2016)
(** contains descriptive animation or video)

 Prerequisites Chapter P.3 Functions Chapter 1:  Limits and Continuity Chapter 2:  Derivatives and Rules of Differentiation 2.1 Slope of the Tangent Line, and Derivative of a Function        geogebra:  Slope of the tangent Line  2.2 Rules of Differentiation  geogebra: derivative practice2.3 Product and Quotient Rules click the printed script for a verbal description of the Product and Quotient Rules 2.4 Chain Rule 2.5 Implicit Differentiation 2.6 Related Rates       geogebra:  Related Rates Introduction Chapter 3:  Applicationsof Differentiation 3.1 Extrema3.2 Rolle's & Mean Value Theorums       geogebra:  Mean Value Theorum3.3 Increasing and Decreasing Functions; 1st Derivative Test     - Understanding f(x) given the 1st derivative: gif 3.4 Concavity and the 2nd Derivative Test     - Comparing f(x) to 1st and 2nd derivative: geogebra    - Derivative Fun 3.5 Limits at Infinity 3.6 Curve Sketching 3.7 Optimization Problems 3.9 Differentials Chapter 4:  Integration 4.1 Antiderivatives and Indefinite Integration 4.2 Area 4.3 Riemann Sums and the Definite Integral geogebra:  Definite Integral and Area VIDEO of geogebra:  Definite Integral and Area 4.4 Fundamental Theorem of Calculus, Pt.1       FTC, Part 2:  MVT Integrals, Ave. Value, 2nd FTC 4.5 Integration by Substitution       Substitution Examples Chapter 5:  Logarithmic, Exponential, and other Transcendental Functions 5.1 The Natural Logarithm:  Definition, Derivative 5.2 The Natural Logarithm & Integration 5.3 Inverse Functions    geogebra:  1. quadratic   2.  ln x     VIDEO of geogebra:     Inverse Functions: an Exploration 5.4 Exponential Functions 5.6 Inverse Trig Functions & Derivatives 5.7 Inverse Trig Functions & Integrals Chapter 6:  Differential Equations 6.1 Differential Equations & Slope Fields 6.2 Differential Equations:  Exponential Growth and Decay 6.3 Separation of Variables & Homogeneous Equations 6.4 First Order Linear Differential Equations Chapter 7:  Application of Integration 7.1 Area of a Region Between Two Curves    geogebra demo 7.2 Volumes of Revolution:  Disk and Washer Method   ** 7.3 Volumes of Revolution:  the Shell Method  **  shell_animation 7.4  Arc Length and Surfaces of Revolution  ** Chapter 8:  Integration Techniques 8.2 Integration by Parts 8.3 Integration with Trig 8.4 Integration with Trig Substitution 8.5 Integration by Partial Fractions 8_7_Indeterminate_Forms_LHopitals

Equation Plotter

Last Updated 01/10/16
By Prof. Battaly, http://www.battaly.com/
Email: merlin@pipeline.com