Lectures + exercises:
Multi-variable Differential and Integral Calculus of Real Functions.
1.Sequence Convergence. Limits, Functions, and Continuity.
2.Total Differential, Partial Derivatives, Directional Derivative, Gradient.
3.Higher Order Differentials, Taylors Polynomial, Taylor’s Theorem.
4.Implicit Function Theorem.
5.Local, Global, and Constrained Extrema, Lagrange multipliers.
6.Double and Triple Integral. Fubini’s Theorem for Double and Triple Integral.
7.Substitution Theorem. Application of Multiple Integrals.
Functions of a Complex Variable.
8.Complex Numbers, Extended Gaussian Images.
9.Complex Functions of a Real and Complex variable.
10.Limits, Continuity, and Complex Functions Derivatives. Conformal Mapping.
11.Complex Function Integration, Cauchy Theorem.
12.Power and Taylor Series. Laurent Series. Rezidue Theorem.
13.Scalar Multiplication, Norm, Orthogonal Systems.
14.Fourier Series.
Multi-variable Differential and Integral Calculus of Real Functions.
1.Sequence Convergence. Limits, Functions, and Continuity.
2.Total Differential, Partial Derivatives, Directional Derivative, Gradient.
3.Higher Order Differentials, Taylors Polynomial, Taylor’s Theorem.
4.Implicit Function Theorem.
5.Local, Global, and Constrained Extrema, Lagrange multipliers.
6.Double and Triple Integral. Fubini’s Theorem for Double and Triple Integral.
7.Substitution Theorem. Application of Multiple Integrals.
Functions of a Complex Variable.
8.Complex Numbers, Extended Gaussian Images.
9.Complex Functions of a Real and Complex variable.
10.Limits, Continuity, and Complex Functions Derivatives. Conformal Mapping.
11.Complex Function Integration, Cauchy Theorem.
12.Power and Taylor Series. Laurent Series. Rezidue Theorem.
13.Scalar Multiplication, Norm, Orthogonal Systems.
14.Fourier Series.