微積分(二)

Course introduction Applications of integrals: area, average

Applications of integrals: volume Improper integrals - The comparison testCourse introduction Applications of integrals: area

Review of differential equations Solving autonomous differential equations: separation of variable Solving nonautonomous differential equations: separation of variableApplications of integrals: average, volume Improper integrals - The comparison test

Quiz 1 Analysis of autonomous differential equations: equilibria Stability theorem for autonomous differential equations Biological examples for autonomous differential equations - Exponential population growth - Logistic population growthReview of differential equations Solving autonomous differential equations: separation of variable Solving nonautonomous differential equations: separation of variable

Systems of autonomous differential equations Predator-prey model Euler’s method to systems of autonomous differential equations Equilibria of systems of autonomous differential equations Phase plane NullclinesQuiz 1 Analysis of autonomous differential equations: equilibria Stability theorem for autonomous differential equations Biological examples for autonomous differential equations - Exponential population growth - Logistic population growth

Phase plane trajectory Direction arrows The dynamics of competition between two speciesSystems of autonomous differential equations Predator-prey model Euler’s method to systems of autonomous differential equations Equilibria of systems of autonomous differential equations Phase plane Nullclines

Quiz 2 Limits and continuity of multivariable functions Partial derivatives Double integrals over rectangles Double integral in polar coordinatesPhase plane trajectory Direction arrows The dynamics of competition between two species

Midterm examQuiz 2 Limits and continuity of multivariable functions Partial derivatives Double integrals over rectangles Double integral in polar coordinates

Deterministic vs. stochastic Sample space and events Set theory Classical definition of probability Axioms of probabilityMidterm exam

Conditional probability - Special cases for conditional probability The law of total probability Bayes’ theoremDeterministic vs. stochastic Sample space and events Set theory Classical definition of probability Probability axioms Conditional probability

Independence Random variables Probability mass function (pmf) Cumulative distribution function (cdf)Special cases for conditional probability The law of total probability Baye’s theorem Independence Random variables

Quiz 3 Expectations of discrete random variables Variances of discrete random variables Bernoulli random variableProbability mass function (pmf) Cumulative distribution function (cdf) Expectations of discrete random variables Variance of discrete random variables Bernoulli random variable

Binomial random variable Geometric random variableQuiz 3 Binomial random variable Geometric random variable

Poisson random variable Continuous random variable Probability density function (pdf) Cumulative distribution function (cdf)Poisson random variable

Quiz 4 Probability density function of a function of a random variable Expectations of continuous random variables Variances of continuous random variablesContinuous random variable Probability density function (pdf) Cumulative distribution function (cdf) Probability density function of a function of a random variable Expectations of continuous random variables Variance of continuous random variables

Uniform random variable Exponential random variableQuiz 4 Uniform random variable Exponential random variable

Normal (Gaussian) random variable

Final exam