Course Description
Mathematics is used widely in chemistry and are absolutely necessary to explore important concepts in chemistry. Mathematics allows a chemist to understand a range of important concepts, model physical scenarios, and solve problems.
Course Content
- Functions of One Variable: Functions, Operators, Differentiation, Integration, Limits, Infinite Series, Power Series
- Complex numbers: Complex Plane, Complex Algebra, Complex roots and powers
- Ordinary Differential Equations: Geometric interpretation, Separable Equations, Linear First Order Equations, Linear Homogenous Equations, Linear Inhomogeneous Equations, Solution by Power Series Expansion, Strum-Liouville Theory, Eigenvalue Eigenfunction Problems
- Vectors and Matrices: Dot Product, Cross Product, Scalar and Vector Fields, Gradient, Divergence and Curl of a Vector Field, Vector Space, Linear Dependence and Basis, Matrices - Properties and Special Matrices, Scalar Functions of Matrices, Determinant, Tensors, Transpose, Adjoint, Inverse, Simultaneous Linear Equations, Diagonalization of a Hermitian Matrix, Matrix Eigenvalue Problem, Matrix Functions
- Functions of Many Variables, Partial Differentiation, Exact Differentials, Multiple Integrals
- Partial Differential Equations: Laplace’s Equation, Heat Flow Equation, Wave Equation, the Schrodinger Equation, Simple Harmonic Oscillator
- Fourier series and Transform, Basic Theorems and Convolution, Laplace Transform and its properties, Applications of Fourier and Laplace Transformations
- Probability and Statistics: Error, Precision, Accuracy, Significant Figures, Mean, Standard Deviation, Normal Distribution, Curve Fitting and Goodness of Fit, Regression, and Correlation
Course Audience
First Year MSc (2 year) Students
Outcomes of this Course
Students will be able to manage and understand most chemical problems as well as measurement and probability aspects as a consequence of this course.