Introductory Mathematical Methods for Biologists

COURSE LAYOUT

Week 1:Introduction, Graphs and Functions

Lecture 1 : Introduction
Lecture 2 : Graphs and Functions
Lecture 3 : Equations as Graphs
Lecture 4 : Exponential and Periodic Functions
Lecture 5 : Logarithmic and Other Functions

Week 2:Functions and its Derivatives, Computing Derivatives of Curves

Lecture 6 : Images as 2D/3D Functions
Lecture 7 : Functions and its Derivatives
Lecture 8 : Computing Derivatives of Curves
Lecture 9 : Rules for Calculating Derivatives
Lecture 10 : Understanding Derivatives

Week 3:Plotting Curves , Numerical Calculation of Derivatives, Partial Derivatives

Lecture 11 : Curvature and Second Derivative
Lecture 12 : Plotting Curves
Lecture 13 : Numerical Calculation of Derivatives
Lecture 14 : Function,Derivatives and Series Expansion
Lecture 15 : L'Hopital's Rule and Partial Derivatives

Week 4:Integration and their Graphical Understanding

Lecture 16 : Integration
Lecture 17 : Integration:Rules
Lecture 18 : Graphical Understanding
Lecture 19 : Integration:More Examples
Lecture 20 : Integration: Product of Two Functions

Week 5:Vectors : Position and Movement in 2D, Cell Symmetry : Use of Polar Coordinates

Lecture 21 : Exponential growth and Decay
Lecture 22 : Scalars and Vectors
Lecture 23 : Vectors:Position and Movement in 2D
Lecture 24 : Cell Symmetry:Use of Polar Coordinates
Lecture 25 : Gradient.Forces and Flows :Part I

Week 6: Gradient, Forces and Flows , Understanding Diffusion

Lecture 26 : Gradient.Forces and Flows :Part II
Lecture 27 : Understanding Diffusion
Lecture 28 : Diffusion Constant and Einstein Relation 1905
Lecture 29 : Diffusion Equation
Lecture 30 : Diffusion vs.Active Transport

Week 7:Introduction to Fourier series , Fourier Transform and Statistics

Lecture 31 : Nernst Equation
Lecture 32 : Fourier Series : Part I
Lecture 33 : Fourier Series : Part II
Lecture 34 : Fourier Transform
Lecture 35 : Introduction to Statistics

Week 8:Basics of bio-statistics

Lecture 36 : Mean,Standard deviation and Distribution
Lecture 37 : Frequency Distribution and Probability Distribution
Lecture 38 : Binomial Distribution
Lecture 39 : Normal Distribution
Lecture 40 : Hypothesis Testing and Mathematical Modeling