1. Antiderivative, indefinite integral and their properties. Integration by parts and using substitutions. 2. Integrating rational functions. 3. Integrating trigonometric functions. Integrating irrational functions. 4. Newton and Riemann integral and their properties. 5. Integration methods for definite integrals. Applications of the definite integral. 6. Geometric and engineering applications of the definite integral. 7. Real function of several variables. Basic notions, composite function. Limits of sequences, limit and continuity of two-functions. 8. Partial derivative, partial derivative of a composite function, higher-order partial derivatives. Total differential of a function, higher-order total differentials. 9. Taylor polynomial of a function of two variables. Local maxima and minima of functions of two variables. 10. Function in one variable defined implicitly. Function of two variables defined implicitly. 11. Some theorems of continuous functions, relative and global maxima and minima. 12. Tangent to a 3-D curve, Tangent plane and normal to a surface. 13. Scalar field, directional derivative, gradient.

1. Differentiating revision. 2. Integration by parts and using substitutions. 3. Integrating rational functions. 4. Integrating trigonometric functions. 5. Integrating irrational functions. 6. Integration methods for definite integrals. 7. Geometric applications of the definite integral. Test 1. 8. Geometric and engineering applications of the definite integral. 9. Partial derivative, partial derivative of a composite function, higher-order partial derivatives. 10. Total differential of a function, higher-order total differentials. Taylor polynomial of a function of two variables. 11. Local maxima and minima of functions of two variables. Test 2. 12. Functions defined implicitly. Global maxima and minima. 13. Tangent plane and normal to a surface. Seminar evaluation.