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1
Maximum & Minimum
2
Turning Points
3
Stationary Points
4
Non-Stationary Turning Points (1 of 2)
5
Non-Stationary Turning Points (2 of 2)
6
Introduction to Points of Inflexion
7
The Special Case of x^4
8
Horizontal Points of Inflexion
9
Overview of Critical Points (1 of 2)
10
Overview of Critical Points (2 of 2)
11
Overview of Critical Points: Examples (1 of 2)
12
Overview of Critical Points: Examples (2 of 2)
13
Finding and Confirming Turning Points
14
Curve Sketching: Locating Stationary Points
15
Curve Sketching: Determining Nature of SPs
16
Curve Sketching: Drawing the Graph
17
Sign of the First Derivative
18
Second Derivative: A Physical Analogy
19
Second Derivative: Concavity
20
Second Derivative: Notation
21
Second Derivative: Relationship w/ First Derivative
22
Graphing w/ the First Derivative
23
Graphing w/ the Second Derivative
24
Choosing First or Second Derivative
25
Graph Behaviour Chart
26
Implicit Differentiation
27
Implicit Differentiation - example question
28
Visual Approach to Derivatives (1 of 2)
29
Visual Approach to Derivatives (2 of 2)
30
Y11 Mathematics Ext 1 Quiz (1 of 2: Curve sketching with calculus)
31
Introduction to Solids of Revolution
32
Verifying Formulae for Cylinder, Cone & Sphere
33
Compound Volumes (1 of 2)
34
Compound Volumes (2 of 2)
35
Volumes: Examples around x-axis & y-axis
36
Subtraction of Volumes
37
Subtraction of Volumes: Class Discussion
38
Volume within a Cone (1 of 3: Separating variables and constants for differentiation)
39
Volume within a Cone (2 of 3: Finding Volume in terms of a single variable to differentiate)
40
Volume within a Cone (3 of 3: Finding the Stationary Points to determine the maximum volume)
41
Solids of Revolution (1 of 3: What happens when you rotate an area around an axis?)
42
Solid of Revolution (2 of 3: Finding Volume of the Solid of Revolution using Volume of a cylinder)
43
Solids of Revolution (3 of 3: Finding the Volume of an area rotated around the y axis)
44
Conical Volume (1 of 2: Derivation of the Volume of a Cone through Solids of Revolution)
45
Spherical Volume (2 of 2: Derivation of the Volume of a Sphere through Solids of Revolution)
46
Difference between Volumes (1 of 2: Method to finding the difference between volumes)
47
Difference Between Volumes (2 of 2: Investigating the relationship between Parabolas & Cylinders)
48
Intro to Solids of Revolution (1 of 3: Establishing the formula)
49
Intro to Solids of Revolution (2 of 3: Simple worked example)
50
Intro to Solids of Revolution (3 of 3: Other axes, volume of a sphere)
51
Solids of Revolution - Subtracting Volumes
52
Non-Standard Integrals: "Differentiate, hence integrate" (1 of 2)
53
Non-Standard Integrals: "Differentiate, hence integrate" (2 of 2)
54
Areas Under Curves: Logarithmic Functions
55
Integration & Logarithmic Functions: Log Integrands (1 of 2)
56
Integration & Logarithmic Functions: Log Integrands (2 of 2)
57
Integration & Logarithmic Functions: Non-Log Integrands (1 of 3)
58
Integration & Logarithmic Functions: Non-Log Integrands (2 of 3)
59
Integration & Logarithmic Functions: Non-Log Integrands (3 of 3)
60
Areas Under Curves: Logarithmic Functions (Alternative Approach)
61
Applications & Implications of d/dx(½v²): Concrete Example
62
Motion Exam Question (1 of 2: Finding v(x) from a(x))
63
Motion Exam Question (2 of 2: Finding x(t) from v(x))
64
Differentiating x^x (3 of 3: Implicit Differentiation)
65
Implicit Differentiation (Differentiating a function without needing to rearrange for x or y)
66
Rates of Change (1 of 4: Finding the Volume of an unknown height of water with a diagram)
67
Maximum/Minimum with Quadratics (1 of 2: Axis of symmetry)
68
Maximum/Minimum with Quadratics (2 of 2: Completing the square)
69
Max/Min Question: Cutting a Wire in Two (1 of 2: Setting up the equations)
70
Max/Min Question: Cutting a Wire in Two (2 of 2: Finding the minimum)
71
Challenging Max/Min Exam Question
72
Graphing Logarithmic Function with Calculus (1 of 2: Identifying features)
73
Graphing Logarithmic Function with Calculus (2 of 2: Constructing the sketch)
74
Differential Equation in terms of Dependent Variable (1 of 2: Partial Fractions)
75
Differential Equation in terms of Dependent Variable (2 of 2: Integration)
Description:
Explore the powerful applications of calculus in this comprehensive 9-hour course. Learn to understand function behavior, visualize characteristics, and solve problems using differential equations. Master concepts like maximum and minimum points, turning points, stationary points, and points of inflection. Dive into curve sketching techniques, implicit differentiation, and solids of revolution. Discover how to apply calculus to real-world scenarios, including motion problems and volume calculations. Develop skills in integrating logarithmic functions, solving differential equations, and tackling challenging maximum/minimum problems. Gain a deep understanding of critical points, derivatives, and their relationships through visual approaches and practical examples.

Applications of Calculus

Eddie Woo
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#Mathematics #Calculus #Differential Equations #Business #Finance #Trading #Derivatives #Logarithmic Functions #Implicit Differentiation
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Maximum & Minimum