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Calculus and Analytical Geometry
Welcome!!
Course Outline
Week Topic
1
• Functions, domain & range. Types of functions
• Composition functions, even and odd functions
2 Limits and Continuity
3
Differential Calculus:
• Concept and Idea of Differentiation
• Geometrical and Physical meaning of Derivatives
• Average Rate of Change
• Derivatives as slope/rate of change
4
Differential Calculus:
• Rules and Techniques of Differentiation
• Tangent and Normal Lines
• Differentiation of Algebraic and Trigonometric
functions
Week Topic
5
Differential Calculus:
• Differentiation of Exponential and Logarithmic functions
• Differentiation of Inverse Trigonometric Functions
• Differentiation of Composite Functions, Chain Rule
6
Implicit Differentiation
• Applications of Differentiation:
• Maxima and Minima of a function
• Concavity
7
Integral Calculus:
• Concept and Idea of Integration
• Indefinite Integral
• Techniques of Integrations (Basic Integration Formula
and Substitution Method)
Course Outline
Week Topic
8
Integral Calculus:
Techniques of Integrations (Integration by Parts)
9
Integral Calculus:
• Techniques of Integrations (Integration by Partial
Fractions)
• Riemann Sum and Definite Integral
10
Applications of Definite Integral:
• Area Between the Curves
• Area of Surface of Revolution
11
Analytical Geometry:
• Introduction to three dimensional Geometry
• 3 Dimensional coordinate systems, Direction
rations, Direction cosines.
Week Topic
12
Analytical Geometry:
• Vectors in Plane
• Vectors in Space
• Dot product
• Cross product
13
Analytical Geometry:
• Vector Calculus
• Divergence of a Vector Field
• Curl of a Vector Field
14
Equation of straight line, intersection of 2 lines,
symmetric form, length of perpendicular from point to a
line.
Angle between lines, Equation of planes
15
Distance between planes, angle between 2 planes
Spherical and Cylindrical Coordinates
Learning Objectives
Understanding of Functions
Types of Functions
Learning Outcomes
Students will be able to define functions
Students will be able to discuss types of functions and their plots
Functions
Calculus by Howard Anton
Functions
Four common methods for representing functions are:
• Numerically by tables • Geometrically by graphs
• Algebraically by formulas • Verbally
Independent and Dependent Variables
y = f(x)
This equation expresses y as a function of x; the variable x is called the independent variable (or
argument)of f, and the variable y is called the dependent variable of f.
Functions
GRAPHS OF FUNCTIONS
Functions
THE VERTICAL LINE TEST
This curve cannot be the graph of a function
Functions
Domain and Range
If x and y are related by the equation y = f(x), then the set of all allowable inputs (x-values) is called the
domain of f, and the set of outputs (y-values) that result when x varies over the domain is called the
range of f.
The projection of y = f(x) on the x-axis is the set of allowable
x-values for f, and the projection on the y-axis is the set of
corresponding y-values.
Functions
• Algebraic Functions
• Trigonometric Functions
• Exponential Functions
• Logarithmic Functions
• Composition of Functions
• Even and Odd Functions
• Piece-Wise Functions
Some of the material in these slides is from Calculus 10/E by
Howard Anton, Irl Bivens, and Stephen Davis
Copyright © 2013 by John Wiley & Sons, Inc. All rights reserved.
Thank you

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calculus Week 1.pptx

  • 3. Course Outline Week Topic 1 • Functions, domain & range. Types of functions • Composition functions, even and odd functions 2 Limits and Continuity 3 Differential Calculus: • Concept and Idea of Differentiation • Geometrical and Physical meaning of Derivatives • Average Rate of Change • Derivatives as slope/rate of change 4 Differential Calculus: • Rules and Techniques of Differentiation • Tangent and Normal Lines • Differentiation of Algebraic and Trigonometric functions Week Topic 5 Differential Calculus: • Differentiation of Exponential and Logarithmic functions • Differentiation of Inverse Trigonometric Functions • Differentiation of Composite Functions, Chain Rule 6 Implicit Differentiation • Applications of Differentiation: • Maxima and Minima of a function • Concavity 7 Integral Calculus: • Concept and Idea of Integration • Indefinite Integral • Techniques of Integrations (Basic Integration Formula and Substitution Method)
  • 4. Course Outline Week Topic 8 Integral Calculus: Techniques of Integrations (Integration by Parts) 9 Integral Calculus: • Techniques of Integrations (Integration by Partial Fractions) • Riemann Sum and Definite Integral 10 Applications of Definite Integral: • Area Between the Curves • Area of Surface of Revolution 11 Analytical Geometry: • Introduction to three dimensional Geometry • 3 Dimensional coordinate systems, Direction rations, Direction cosines. Week Topic 12 Analytical Geometry: • Vectors in Plane • Vectors in Space • Dot product • Cross product 13 Analytical Geometry: • Vector Calculus • Divergence of a Vector Field • Curl of a Vector Field 14 Equation of straight line, intersection of 2 lines, symmetric form, length of perpendicular from point to a line. Angle between lines, Equation of planes 15 Distance between planes, angle between 2 planes Spherical and Cylindrical Coordinates
  • 5. Learning Objectives Understanding of Functions Types of Functions Learning Outcomes Students will be able to define functions Students will be able to discuss types of functions and their plots
  • 7. Functions Four common methods for representing functions are: • Numerically by tables • Geometrically by graphs • Algebraically by formulas • Verbally Independent and Dependent Variables y = f(x) This equation expresses y as a function of x; the variable x is called the independent variable (or argument)of f, and the variable y is called the dependent variable of f.
  • 9. Functions THE VERTICAL LINE TEST This curve cannot be the graph of a function
  • 10. Functions Domain and Range If x and y are related by the equation y = f(x), then the set of all allowable inputs (x-values) is called the domain of f, and the set of outputs (y-values) that result when x varies over the domain is called the range of f. The projection of y = f(x) on the x-axis is the set of allowable x-values for f, and the projection on the y-axis is the set of corresponding y-values.
  • 11. Functions • Algebraic Functions • Trigonometric Functions • Exponential Functions • Logarithmic Functions • Composition of Functions • Even and Odd Functions • Piece-Wise Functions
  • 12.
  • 13. Some of the material in these slides is from Calculus 10/E by Howard Anton, Irl Bivens, and Stephen Davis Copyright © 2013 by John Wiley & Sons, Inc. All rights reserved.