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ON – Study Materials & Exercises | Math 12 (Calculus and Vectors)

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Unit.1 Introduction to Calculus

7 Topics

1.1 Radical Expression

1.2 Slope of Tangent Line

1.3 Rate of Change

1.4 Limit of a Function

1.5 Properties of Limits

Solution 1.1-1.6

Unit.2 Derivatives

6 Topics

2.1 Derivative Functions

2.2 Derivative of Polynomial Functions

2.3 Product Rule

2.4 Quotient Rule

2.5 Derivative of Composite Functions

Solution 2.1-2.5

Unit.3 Applications of Derivatives

5 Topics

3.1 Higher Order of Derivatives, Velocity and Acceleration

3.2 Maximum and Minimum

3.3 Optimization Problem I

3.4 Optimization Problem II

Solutions 3.1-3.4

Unit.4 Curve Sketching

6 Topics

4.1 Increasing and Decreasing Functions

4.2 Critical Points Local Maxima and Minima

4.3 Vertical and Horizontal Asymptotes

4.4 Concavity and Point of Inflection

4.5 Algorithm for Curve Sketching

Solution 4.1-4.5

Unit.5 Derivative of Exponential and Trigonometry Functions

5 Topics

5.1 Derivative of Exponential Function

5.2 Derivative of Exponential Functions Con’t

5.3 Optimization Problem with Exponential Functions

5.4 Derivative of Trigonometry Functions

5.5 Derivative of Trigonometry Functions Con’t

Unit.6 Introduction to Vectors

9 Topics

6.1 Introduction to Vectors

6.2 Vector Addition

6.3 Vector Multiplication by a Scalar

6.4 Properties of Vectors

6.5 Vectors in R2 R3

6.6 Operation with Algebraic Vectors in R2

6.7 Operation with Vectors in R3

6.8 Linear Combination and Spanning Sets

Solution 6.1-6.8

Unit.7 Applications of Vectors

7 Topics

7.1 Vector as Force

7.2 Vector as Velocity

7.3 Dot Product of Two Geometric Vectors

7.4 Dot Product of Algebraic Vectors

7.5 Scalar Vector Projections

7.6 Cross Product of Two Vectors

7.7 Applications Dot and Cross Products

Unit.8 Equations of Lines and Planes

7 Topics

8.1 Vector and Parametric Equations of Line in R2

8.2 Cartesian Equation of a Line

8.3 Vector Parametric and Symmetric Equation in a Line in R3

8.4 Vector and Parametric of a Plane

8.5 The Cartesian Equation of a Plane

8.6 Sketching in R3

Solution 8.1-8.6

Unit.9 Relationships between Points Lines and Planes

6 Topics

9.1 Intersection of Line and Plane

9.2 System of Equations

9.3 Intersection of 2 Planes

9.4 Intersection of 3 Planes

9.5 Distance from a Point to Line in R2 R3

9.6 Distance from a Point Line

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