This is a compulsory course aimed at Chemistry and Earth Sciences students at the second semester of their first bachelor year. The course intends to provide the students with the mathematical tools they need in studying courses in chemistry and physics. Upon successful completion of the course, the students should be familiar with the main mathematical concepts and methods in many-variable calculus, vector analysis and ordinary differential equations, and be able to apply them to problems in chemistry.
The topics of the course include:
1. Overview: vectors – addition, subtraction, scalar and vector products.
2. Many-variable functions: partial derivatives, directional derivative. Examples in chemistry.
3. Vector and scalar fields. Derivatives of vectors. Gradient. Examples in physics and chemistry.
4. The operator nabla. Divergence, curl and laplacian. Examples.
5. Analysis of a many-variable function: minima, maxima, saddle points. Constraints and Lagrange multipliers.
6. Integral of a many-variable function. Change of variables, Jacobian. Examples and applications.
7. Line integrals, conserving fields. Surface integrals. Flux.
8. Green, Gauss and Stokes theorems.
9. Spherical and cylindrical coordinates. Gradient, divergence and Laplacian in these coordiantes.
10. Ordinary differential equations (ODEs). Types and common examples in chemistry and physics.
11. First order ODEs. Selected solution methods. Initial conditions.
12. Second order ODEs. Solution independence. Homogeneous and inhomogeneous ODEs.
Mastering the course topics detailed above is achieved not only by understanding the derivation of the concepts in class, but – most importantly – by systematic practice, performing exercises during the TA sessions and at home.
Methodologically, this course relies on the course Mathematics for Chemistry and Earth Sciences Students (1) and somewhat on the course Mechanics for Chemists, both given during the 1st semester. The material provided in the course is relevant to the courses in Electricity an Magnetism, Thermodynamics, Physical Chemistry, Introduction to the Chemical Bond, and many more.