__Support materials__

- Mathematical rigor
- Numbers
- Real functions
- Elementary functions - graphs
- Continuity and limits of functions
- Derivatives
- Parametric equations of planar curves
- Integrals
- Differential equations

__Slides from lecture__

- Introduction
- Real functions
- Continuity and limits of functions
- Derivatives
- Graphing functions
- Taylor polynomial, differential
- Parametric equations of planar curves
- Integral calculus
- Definite integral
- Applications of integrals
- Differential equations of the first order
- Linear differential equations with constant coefficients
- Applications of differential equations

__Syllabus __ – here

- Functions of a single real variable. Domain and range. Graphs of elementary functions. Basic properties. Composition of functions.
- Inverse functions. Exponential and logarithmic functions. Trigonometric and inverse trigonometric functions.
- Continuity of a function. Properties of continuous functions. Limits of sequences and functions.
- Derivatives. Geometrical and physical meaning of derivatives. Rules for computing derivatives. Differential of a function.
- Physical and geometrical applications of derivatives. L’Hospital’s rule. Approximation of a function value using Taylor polynomial. Analysis and graphing of a function.
- Numerical solution of an equation of a single uknown variable - Newton’s method. Parametric curves, tangent vector to a curve.
- Antiderivatives and their properties. Newton definite integral, its properties and geometrical meaning.
- Methods for computing indefinite and definite integrals – integration by parts and substitution method.
- Integration of rational functions. Improper integrals. Numerical integration – trapezoidal method.
- Riemann definite integral. Selected geometrical and physical applications of the integral.
- Differential equations. Terminology, general and particular solution. Separation of variables.
- First order linear differential equations. Variation of constants. Numerical solution of a first order differential equations – Euler’s method.
- Second order linear differential equations with constant coefficients and a special right-hand. Estimation method.
- Application of differential equations in Physics, Chemistry, and Biochemistry. Revision and discussion.

__Consultations__ – by agreement personal or email