New Approach to Higher Mathematics

K.KUMARAVELU, Mar 9, 2022

இந்த புத்தகத்தில், GeoGebra மென்பொருளைப் பயன்படுத்தி கணிதக் கருத்துகளை எவ்வாறு காட்சிப்படுத்துவது என்பதைக் கற்றுக்கொள்வோம். In this book, we will learn how to visualize mathematical concepts using GeoGebra software.

Table of Contents

  1. Relations and Functions
    1. Value of Function at a point
  2. Graphing functions using transformations
    1. Shifting of Graphs
    2. Shifting of graphs f(x+a)
    3. Reflection of a graph -f(x)
    4. Even or Odd function
    5. Translations of graphs f(x+a)+a, f(x-a)-a
  3. Complex numbers
    1. Algebraic operations on Complex Numbers
    2. Addition of two Complex Numbers
    3. Subtraction of two Complex Numbers
  4. Matrices and Determinants
    1. Algebraic Operations on Matrices - Order 3
    2. Algebraic Operations on Matrices
    3. Activity - Determinants
    4. Test for consistency of the system of linear equations
    5. Test of consistency of the system of linear equations
    6. test for consistency of the system of linear equations
    7. Limit of a function at a point
  5. Vectors
    1. addition of two vectors
    2. Addition of two Vectors in Three Dimensional
  6. Permutation and Combination
    1. Permutations
  7. Differential Calculus
    1. Derivative of a Function
    2. Limit of a function at a point
  8. Straight lines
    1. General form of Straight line ax+by+c=0
    2. Intersection of two lines
  9. Quadratic Equations
    1. Vieta's Formula for Quadratic Equations
  10. Integral Calculus
    1. Properties of Integrals

1.

Relations and Functions

  • 1. Value of Function at a point

1.1.

Value of Function at a point

Value of a Function
– K.KUMARAVELU

2.

Graphing functions using transformations

  • 1. Shifting of Graphs
  • 2. Shifting of graphs f(x+a)
  • 3. Reflection of a graph -f(x)
  • 4. Even or Odd function
  • 5. Translations of graphs f(x+a)+a, f(x-a)-a

2.1.

Shifting of Graphs

Shifting of graphs f(x)+a
– K.KUMARAVELU

2.2.

–

2.3.

–

2.4.

–

2.5.

–

3.

Complex numbers

  • 1. Algebraic operations on Complex Numbers
  • 2. Addition of two Complex Numbers
  • 3. Subtraction of two Complex Numbers

3.1.

Algebraic operations on Complex Numbers

sum and difference of two complex numbers.[br]try to find the product of two complex numbers using the input command[br]z_1*z_2
– K.KUMARAVELU

3.2.

–

3.3.

–

4.

Matrices and Determinants

  • 1. Algebraic Operations on Matrices - Order 3
  • 2. Algebraic Operations on Matrices
  • 3. Activity - Determinants
  • 4. Test for consistency of the system of linear equations
  • 5. Test of consistency of the system of linear equations
  • 6. test for consistency of the system of linear equations
  • 7. Limit of a function at a point

4.1.

Algebraic Operations on Matrices - Order 3

Algebraic Operations on Matrices -Order 3 by 3
[color=#0000ff]Basic operations on Matrices are[/color][br][br]1. Multiplication of a Matrix by a scalar, [br]2. Addition / Subtraction of two Matrices, and [br]3. Multiplication of two Matrices[br][br][br][color=#ff0000]NOTE:[/color] There is no concept of dividing a matrix by another matrix and thus, the operation [math]\frac{A}{B}[/math] , where [math]A[/math] and [math]B[/math] are matrices, is not defined
– K.KUMARAVELU

4.2.

–

4.3.

–

4.4.

–

4.5.

–

4.6.

–

4.7.

–

5.

Vectors

  • 1. addition of two vectors
  • 2. Addition of two Vectors in Three Dimensional

5.1.

addition of two vectors

– K.KUMARAVELU

5.2.

–

6.

Permutation and Combination

  • 1. Permutations

6.1.

Permutations

– K.KUMARAVELU

7.

Differential Calculus

  • 1. Derivative of a Function
  • 2. Limit of a function at a point

7.1.

Derivative of a Function

Derivative of a function at a point
Derivative of a function at a point is the slope of the tangent to the corresponding curve at that point.
– K.KUMARAVELU

7.2.

–

8.

Straight lines

  • 1. General form of Straight line ax+by+c=0
  • 2. Intersection of two lines

8.1.

General form of Straight line ax+by+c=0

General form of Straight line ax+by+c=0
– K.KUMARAVELU

8.2.

–

9.

Quadratic Equations

  • 1. Vieta's Formula for Quadratic Equations

9.1.

Vieta's Formula for Quadratic Equations

– K.KUMARAVELU

10.

Integral Calculus

  • 1. Properties of Integrals

10.1.

Properties of Integrals

– K.KUMARAVELU

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