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Master Calculus 1

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87 core skills 100% total weight

01

Connecting f, f', and f''

02

EVT, Extrema & Critical Points

03

Implicit Relation Behaviors

04

Candidates Test for Global Extrema

05

Determining Concavity

06

First Derivative Test

07

Increasing/Decreasing Intervals

08

Intro to Optimization

09

Second Derivative Test

10

Solving Optimization Problems

11

Graphing Functions & Derivatives

12

Mean Value Theorem

13

Motion: Position, Velocity, Acceleration

14

Non-Motion Rates of Change

15

Intro to Related Rates

16

Related Rates with Geometry

17

Solving Related Rates

18

Derivative Meaning in Context

19

L'Hospital's Rule

20

Linear Approximation

21

Area Between Curves (x-functions)

22

Area Between Curves (y-functions)

23

Area Between Multiple Intersections

24

Cross Sections: Squares & Rectangles

25

Cross Sections: Triangles & Semicircles

26

Disc Method: Other Axes

27

Disc Method: x- or y-Axis

28

Washer Method: Other Axes

29

Washer Method: x- or y-Axis

30

Accumulation Functions in Context

31

Average Value of a Function

32

Position, Velocity, Acceleration via Integrals

33

Work & Fluid Force

34

35

Higher-Order Derivatives

36

Selecting Derivative Procedures

37

Differentiating Inverse Functions

38

Inverse Trig Derivatives

39

Implicit Differentiation

40

Basic Derivative Rules

41

Derivative Definition & Notation

42

Derivatives of cos, sin, e^x, ln x

43

Derivatives of tan, cot, sec, csc

44

Differentiability & Continuity

45

Estimating Derivatives

46

Average & Instantaneous Rates

47

48

49

50

Derivatives of sin & cos

51

Derivatives of tan & Other Trig

52

Exponential DE Models

53

Modeling with Differential Equations

54

Verifying DE Solutions

55

General Solutions: Separation of Variables

56

Particular Solutions: Initial Conditions

57

Reasoning with Slope Fields

58

Sketching Slope Fields

59

Antiderivatives & Indefinite Integrals

60

Basic Trig Integrals

61

FTC & Accumulation Functions

62

FTC & Definite Integrals

63

Accumulation Function Behavior

64

Accumulations of Change

65

Integration: Long Division & Completing Square

66

Properties of Definite Integrals

67

Selecting Integration Techniques

68

Riemann Sum Approximations

69

Riemann Sums & Notation

70

Integration by Substitution

71

72

Continuity at a Point

73

Continuity over an Interval

74

Intermediate Value Theorem

75

Removing Discontinuities

76

Types of Discontinuities

77

Estimating Limits from Graphs

78

Estimating Limits from Tables

79

Infinite Limits & Vertical Asymptotes

80

Limit Definition & Notation

81

Limits at Infinity & Horizontal Asymptotes

82

Limits via Algebraic Manipulation

83

Limits via Algebraic Properties

84

Multiple Limit Representations

85

Selecting Limit Procedures

86

Squeeze Theorem

87

Intro to Calculus: Instantaneous Change