CALCULUS:   Class Notes - New Syllabus

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

    Test # 1 Preparation
OS Chapter 1   Functions
OS:  OpenStax
Chapter 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 Point
Ch 3.2 Derivative as a Function
Ch 3.3 Derivatives: Basic Rules
Ch 3.3 Derivatives: Product and Quotient Rules
Ch 3.4 Derivatives as Rates of Change
Ch 3.5 Derivatives of Trig Functions
Ch 3.6 The Chain Rule for Composite Functions
Ch 3.8 Implicit Differentiation
Ch 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 1
5.4  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 
       videos: Shell Method   Shell Method-3D
                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

Equation Plotter

Last Updated 12/12/18
By Prof. Battaly,