teaching

Present courses

Integral calculus

1. Antiderivatives and indefinite integrals
2. Techniques of integration
   2.1 Integration by substitution
   2.2 Integration by parts
   
3. The Riemann Integral
   3.1 Definition and existence
   3.2 Properties of the integral
   3.3 The fundamental theorem of calculus
   3.4 Areas between curves
   3.5 The mean value theorem for integrals
   3.6 Improper integrals
   3.7 Applications to business and economics
   

Functions of several variables

1. Domains, ranges, graphing, level curves and contur maps
2. Limits and continuity
3. Partial derivatives
4. Tangent planes and linear approximations
5. The chain rule
6. Implicit differentiation
7. Direccional derivatives and linear approximations
8. Maxima/minima problems
9. Lagrange multipliers

Previous courses

Linear Algebra

1. Systems of linear equations
   1.1 Augmented matrix
   1.2 Gaussian elimination
   1.3 Homogeneous systems
2. Matrices
   2.1 Operations with matrices
   2.2 Row operations
   2.3 Inverse matrix
   
3. Determinants
   3.1 Determinant of 2x2 and 3x3 matrices
   3.2 Minors and cofactors of a square matrix
   3.3 The cofactor expansion
   3.4 Properties of determinants
   3.5 Cramer’s rule
4. Vector spaces
   4.1 Vector space, subspace
   4.2 Linear combination, linear independence
   4.3 Basis and dimension of a vector space
   4.4 Change of basis
5. Linear transformations
   5.1 Linear transformation and matrices for linear transformations
   5.2 Kernel and range of a linear transformation
   5.3 Change of basis
6. Eigenvalues and eigenvectors
   6.1 Definition
   6.2 Diagonalization
   6.3 Symmetric matrices and orthogonal diagonalization
   

Multiple integration

1. Double integrals over rectangular regions
   
2. Double integrals over general regions
   
3. Double integrals in polar coordinates
   
4. Triple integrals
   
5. Change of variables
   

Introduction to differential equations

1. Basics of differential equations
   1.1 Separable equations
   1.2 The logistic equation
   1.3 First-order linear equations
2. Second-order differential equations
   2.1 Second-order linear equations
   2.2 Nonhomogeneous linear equations
   

Sequences and series

1. Sequences
   
2. Infinite series
   
3. The divergence and integral tests
   
4. Comparison tests
   
5. Alternating series
   
6. Ratio and root tests
   
7. Power series
   7.1 Power series and functions
   7.2 Properties of power series
   7.3 Taylor and Maclaurin series
   

Descriptive statistics and probability theory

1. Introduction to statistics
   1.1 Primary and secondary data
   1.2 Methods of collection and editing of data
   
2. Measures of central tendency
   2.1 Mean
   2.2 Median
   2.3 Mode
   2.4 Geometric mean
   2.5 Harmonic mean
   
3. Measures of dispersion
   3.1 Range
   3.2 Quartile deviation, mean deviation and standard deviation
   3.3 Central and non-central moments
   3.4 Sheppard’s correction
   3.5 Skewness and kurtosis
   
4. Introduction to probabilities
   4.1 Basic concepts: random experiments, trial, outcome, sample space, event
   4.2 Mutually exclusive and exhaustive events
   4.3 Equally likely and favourable outcomes
   4.4 Definitions of probability
   4.5 Baye’s theorem: conditional probability and independence of events
   
5. Random variables
   5.1 Definition: discrete and continuous random variables, functions of random variables
   5.2 Probability mass function, probability density function, distribution function and its properties
   5.3 Bivariate random variable