# CALCULUS:  Class Notes - New Syllabus

Prof.  G. Battaly, Westchester Community College, Valhalla NY  (updated 12/12/2018)

 Test # 1 Preparation OS Chapter 1 Functions OS:  OpenStaxChapter 2: Limits 2.1  Tangent, Velocity, Area       geogebra:  Tangent Line 2.2  Limits and 2.3 Evaluating Limits       geogebra:  Special Indeterminante Limit: [sin x]/x 2.4  Continuity Chapter 3:  Derivatives Ch 3.1 Derivative at a PointCh 3.2 Derivative as a FunctionCh 3.3 Derivatives: Basic RulesCh 3.3 Derivatives: Product and Quotient RulesCh 3.4 Derivatives as Rates of ChangeCh 3.5 Derivatives of Trig FunctionsCh 3.6 The Chain Rule for Composite FunctionsCh 3.8 Implicit DifferentiationCh 3.9 Exponential and Logarithmic Functions Chapter 4: Applications Ch 4.1 Related Rates   Ch 4.2 Differentials and Approximations   Ch 4.3 Critical Values and Extrema Ch 4.4 Mean Value Theorum   Ch 4.5 1st and 2nd Derivative Tests, Concavity   Functions and Derivatives: Graphs of f(x), f '(x), f ''(x)   Ch 4.6 Limits at Infinity and Asymptotes  Given graph of f '(x) Find graph of f(x) [gif animation]   Ch 4.7 Optimization Problems   Ch 4.8 L'Hopital's Rule    Ch 4.10 Antiderivatives, Indefinite Integrals Chapter 5:  Integration VIDEO of geogebra:  Definite Integral and Area  Definite Integral and Area - mp4 video file for mobile geogebra:  Definite Integral and Area 5.1  Area under a Curve 5.2  Definite Integral 5.3  Fundamental Theorum of Calculus _Part 1 5.3  Fundamental Theorum of Calculus _Part 2 STEWART "Calculus" 8th ed.Quick Review of Calc 15.4  Indefinite Integral; FTC asNet Change 5.5  Integration by Substitution Chapter 6:  Applications of Integration 6.1 Area between Two Curves      geogebra:  Area betw Two Curves   6.2 Volume-Disk Method & Cross Section videos: Disk Method  Disk Method-3D                Solid from circles-around x Axis                Solid: sqrt(x)-around y Axis                Solid: Xsection -base ellipse, triangles 6.3 Volume-Shell Method                         Shell: 2 curves around x=2 6.5 Mean Value Theorum, Integrals & Average Value Chapter 7: 7.1 Integration by Parts         Reading: Applications in Engineering 7.2 Trigonometric Integrals 7.3 Integration by Trig Substitution 7.4 Integration by Partial Fractions 7.5 Strategy:  Which Approach? 7.6 CAS, tables 7.7 Approximate Integration 7.8 Improper Integrals Integral with Infinite Limit - Video     Powerpoints: Introduction, Definition Chapter 8 : 8.1 Arc Length Chapter 11 : 11.1 Sequences       *** Series/Tests Summary Chart *** 11.2 Series 11.3 and 11.4 Integral Test, Direct Comparison & Limit Tests Helpful sites: 11.5 Alternating Series & 11.6 Ratio and Root Tests Convergence: R, IC 11.8 Power Series & 11.9 Functions as Power Series Find Taylor Series 11.10 Taylor and Maclaurin Series

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Last Updated 12/12/18
By Prof. Battaly, http://www.battaly.com/
Email: merlin@pipeline.com