## About Your trainer

At first glance, Pavan Kumar AV is pursuing a Ph.D. from IMT school of advanced studies, Lucca. Nearly eight years have now passed since the young Pavan set about his task of clarifying mathematics, extending it, applying it wherever possible, and placing it on a firm theoretical footing. His career stands out as one of the most brilliant, versatile, in the annals of Mathematics.

Realizing the central role of Mathematics and physics, he took many projects ranging from engineering like“SAE SUPRA India”, “Arthrobotix”, ” Studsat” “power generator using a Speed Breaker” was presented at the “IEEE Humanitarian Technology conference 2014 (Student paper)”, “Development of a Real-Time Human Tracking Capability on a Mobile Platform” to pure mathematics such as ” Meta Stability and sloe motion dynamics of Cahn-Hilliard equation “, ” Phase-field approximation and published more than 10 research papers. He was awarded a “Gold medal“ for getting the highest marks and the “Best Outgoing Student Award”. He graduated with a Master’s degree in Erasmus Mundus Joint Master’s degree program in Applied Mathematics (MathMods).

Now he aims to build and work in a research lab of his own in India, after gaining experience and expertise working on various aspects of PDEs

## Some Serious Questions

1. Why are some mathematicians crazy about prime numbers?

2. Is it natural to see primes in parametric equation?

3. Does this also means, there is a connection between everything and everything else?

4. Do you just want to see them in 3D?

### Total Hours : 20

Time: Monday and Wednesday, 2 hours Per Session

Date : Jan 18 to Feb 17

#### What is this course not about:

- This is not to teach you how to solve problem
- This is not crash course in math
- This is not a syllabus of any university
- This is not to teach you any specific software
- This is not about computation

#### What you learn:

1. Henry Poincare once said “It is by logic we prove, but by intuition we discover”

2. Build intuition to mathematics, to be able to see equation and understand them.

3. To be able to connect the mathematics with the world (Engineering, Physics)

4. Practical application of each mathematical concepts.

5. To be able to manipulate and create your own graphs and understand new mathematical ideas.

#### What is this course about:

1. This course is to build intuition of mathematics systemically.

2. This course enable to you understand the concepts.

3. This course is about revisiting the things you learned in mathematics with unique perspectives of graphics

and animation.

#### Course Content Overview

### Basics Functions (Introduction to Imagination)

1. Functions

2. Straight Line

3. Can You See Solutions?

4. Quadratic Equation

5. Polynomial Equations

6. Trig Functions

7. Generation of Skin Curves

8. Odd and Even Functions

9. Power Functions

10. Can You See Theorem Too?

### Play With Functions

1. Addition and Subtraction of Functions

2. Multiplication, Division and Inverse

3. Fourier Series

4. Approximation of Functions.. Why Fourier?

5. Can You Draw a Cat?

6. Dirac Delta (Basic Function For Quantum Mechanics)

7. Parametric Equations

8. Implicit Functions

9. Polar Functions

10. Some Arts Session

11. Now Butterfly is Something you Understand

12. Take my Heart

### Derivative

1. Limits

2. Continuity

3. Rules of Continuity

4. Asymptotic Behaviors

5. Cauchy Sequence

6. Continuity

7. Derivatives

8. Perspective is Everything in Differentiation

9. Taylor Series and Maclauran Series

10. Mean Value Theorem

11. Squeeze Theorem

### Linear Algebra

1. Wait? Can You See a Matrix? Of course Yes!

2. Multiplication of Matrix

3. Basis Functions

4. Transformation

5. Eigenvalue

6. Eigen Vector

7. Determinant

8. Change of Basis (Orthogonal, Orthonormal)

### Vector Calculus

1. Vector Field

2. Scalar Field

3. Gradients

4. Divergence

5. Curl

6. Directional Derivative

7. Steepest Ascent

8. Slope Field

9. Integration by Parts

10. Initial Value Problem

11. Partial Derivative

12. Laplacian