Science:Math Exam Resources/Courses/MATH105

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MATH105



General Course Info

Visit the course main page here.


Available Practice Exams

Dynamic Course Syllabus

Week 1. Functions of several variables (Chapter 12)

  • Planes and surfaces (12.1)
  • Graphs and level curves (12.2)

Learn about multivariable calculus

Learn about level curves


Week 2. Functions of several variables (Chapter 12)

  • Partial derivatives (12.4)
  • Maximum/minimum problems (12.8)

Learn about partial derivatives

Learn about optimization

Learn about multivariable calculus


Week 3. Functions of several variables (Chapter 12)

  • Maximum/minimum problems (12.8)
  • Lagrange multipliers (12.9)

Learn about optimization

Learn about Lagrange multipliers


Week 4. Integration (Chapter 5)

  • Approximating areas under curves (5.1)
  • Definite integrals (5.2)

Learn about Riemann sums

Learn about integration using symmetry

Learn about antiderivative sketching

Learn about calculating the area between two curves


Week 5. Integration (Chapter 5)

  • Fundamental theorem of calculus (5.3)
  • Substitution rule (5.5)
  • Integration by parts (7.1)

Learn about the Fundamental Theorem of Calculus

Learn about substitution

Learn about integration by parts


Week 6. Integration techniques (Chapter 7)

  • Trigonometric Integrals (7.2)
  • Trigonometric substitutions (7.3)
  • Partial fractions (7.4)

Practice integrals uncategorized, based on any technique

Learn about trigonometric integrals

Learn about trigonometric substitutions

Learn about partial fractions


Week 7. Integration techniques (Chapter 7)

  • Numerical integration (7.6)
  • Improper integrals (7.7)
  • Introduction to differential equations (7.8)

Learn about the trapezoidal rule

Learn about the Simpson's rule

Learn about improper integrals

Learn about the integral comparison test

Learn about separation of variables

Learn about integrals that cycle

Learn about differential equations

Learn about initial value problems

Learn about equilibrium

Learn about steady states


Week 8. Probability (Probability Appendix)

  • Random Variables and Probability Basics (1.1, 1.2 and 1.4 in Probability Appendix)
  • Continuous random variable (2.1, 2.2 and 2.3 in Probability Appendix)
  • Expected Value, Variance, and Standard Derivation (2.5 and 2.6 in Probability Appendix)

Learn about probability density functions

Learn about the standard deviation

Learn about the mean

Learn about the median

Learn about cumulative distribution functions

Learn about discrete probability


Week 9. Sequences and infinite series (Chapter 8)

  • Sequences (8.1-8.2)
  • Infinite series (8.3)
  • The divergence and integral tests (8.4)

Learn about sequences

Learn about series

Learn about power series

Learn about the integral comparison test


Week 10. Series (Chapter 8) and Power series (Chapter 9)

  • The ratio, root and comparison tests (8.5).
  • Approximating functions with polynomials (9.1)
  • Properties of power series (9.2)

Learn about series

Learn about power series


Week 11. Power series (Chapter 9) and review

  • Taylor series (9.3)
  • Working with Taylor series (9.4)

Learn about power series

Learn about Taylor series

All Topics in this Course in Alphabetical Order

MER QGH flag, MER QGQ flag, MER QGS flag, MER QGT flag, MER Tag Partial derivative---MER QGH flag, MER QGQ flag, MER QGS flag, MER QGT flag, MER Tag Partial derivative---MER QGH flag, MER QGQ flag, MER QGS flag, MER QGT flag, MER Tag Optimization---MER QGH flag, MER QGQ flag, MER QGS flag, MER QGT flag, MER Tag Substitution---MER QGH flag, MER QGQ flag, MER QGS flag, MER QGT flag, MER Tag Substitution---MER QGH flag, MER QGQ flag, MER QGS flag, MER QGT flag, MER Tag Integration by parts---MER CH flag, MER CS flag, MER QGQ flag, MER QGT flag, MER Tag Solid of revolution---MER QGH flag, MER QGQ flag, MER QGS flag, MER QGT flag, MER Tag Improper integral---MER CH flag, MER CS flag, MER QGQ flag, MER QGT flag, MER Tag Riemann Sum---MER QGH flag, MER QGQ flag, MER QGS flag, MER RT flag, MER Tag Multivariable calculus---MER QGH flag, MER QGQ flag, MER QGS flag, MER QGT flag, MER Tag Multivariable calculus, MER Tag Partial derivative---MER QGH flag, MER QGQ flag, MER QGS flag, MER RT flag, MER Tag Fundamental theorem of calculus---MER QGH flag, MER QGQ flag, MER QGS flag, MER RT flag, MER Tag Riemann sum---MER QGH flag, MER QGQ flag, MER QGS flag, MER QGT flag, MER Tag Riemann sum---MER QGH flag, MER QGQ flag, MER QGS flag, MER QGT flag, MER Tag Solid of revolution---MER QGH flag, MER QGQ flag, MER QGS flag, MER RT flag, MER Tag Substitution---MER QGH flag, MER QGQ flag, MER QGS flag, MER RT flag, MER Tag Integration by parts---MER QGH flag, MER QGQ flag, MER QGS flag, MER RT flag, MER Tag Trapezoidal rule---MER QGH flag, MER QGQ flag, MER QGS flag, MER RT flag, MER Tag Differential equation---MER QGH flag, MER QGQ flag, MER QGS flag, MER RT flag, MER Tag Probability density function---MER QGH flag, MER QGQ flag, MER QGS flag, MER RT flag, MER Tag Cumulative distribution function---MER QGH flag, MER QGQ flag, MER QGS flag, MER RT flag, MER Tag Variance---MER QGH flag, MER QGQ flag, MER QGS flag, MER RT flag, MER Tag Consumer surplus---MER QGH flag, MER QGQ flag, MER QGS flag, MER RT flag, MER Tag Area between two curves---MER QGH flag, MER QGQ flag, MER QGS flag, MER RT flag, MER Tag Lagrange multipliers---MER QGH flag, MER QGQ flag, MER QGS flag, MER RT flag, MER Tag Differential equation---MER QGH flag, MER QGQ flag, MER QGS flag, MER RT flag, MER Tag Differential equation, MER Tag Initial value problem---MER QGH flag, MER QGQ flag, MER QGS flag, MER RT flag, MER Tag Differential equation---MER QGH flag, MER QGQ flag, MER QGS flag, MER RT flag, MER Tag Riemann sum---MER QGH flag, MER QGQ flag, MER QGS flag, MER RT flag, MER Tag Integrals that cycle---MER QGH flag, MER QGQ flag, MER QGS flag, MER RT flag, MER Tag Trigonometric integral---MER QGH flag, MER QGQ flag, MER QGS flag, MER RT flag, MER Tag Area between two curves---MER QGH flag, MER QGQ flag, MER QGS flag, MER RT flag, MER Tag Probability density functions---MER QGH flag, MER QGQ flag, MER QGS flag, MER RT flag, MER Tag Consumer surplus, MER Tag Market equilibrium---MER QGH flag, MER QGQ flag, MER QGS flag, MER RT flag, MER Tag Differential equation, MER Tag Initial value problem---MER QGH flag, MER QGQ flag, MER QGS flag, MER RT flag, MER Tag Differential equation, MER Tag Initial value problem---MER QGH flag, MER QGQ flag, MER QGS flag, MER RT flag, MER Tag Differential equation---MER QGH flag, MER QGQ flag, MER QGS flag, MER RT flag, MER Tag Optimization---MER QGH flag, MER QGQ flag, MER QGS flag, MER RT flag, MER Tag Optimization---MER QGH flag, MER QGQ flag, MER QGS flag, MER RT flag, MER Tag Marginal productivity---MER QGH flag, MER QGQ flag, MER QGS flag, MER RT flag, MER Tag Linear approximation, MER Tag Marginal productivity---MER QGH flag, MER QGQ flag, MER QGS flag, MER RT flag, MER Tag Gradients, MER Tag Marginal productivity---MER QGH flag, MER QGQ flag, MER QGS flag, MER RH flag, MER RT flag, MER Tag Limit of a function, MER Tag Multivariable calculus---MER QGH flag, MER QGQ flag, MER QGS flag, MER RT flag, MER Tag Fundamental theorem of calculus---MER QGH flag, MER QGQ flag, MER QGS flag, MER RT flag, MER Tag Riemann sum---MER QGH flag, MER QGQ flag, MER QGS flag, MER RT flag, MER Tag Improper integral---MER QGH flag, MER QGQ flag, MER QGS flag, MER RT flag, MER Tag Level curves---MER QGH flag, MER QGQ flag, MER QGS flag, MER RT flag, MER Tag Power series---MER QGH flag, MER QGQ flag, MER QGS flag, MER RT flag, MER Tag Geometric series, MER Tag Power series---MER QGH flag, MER QGQ flag, MER QGS flag, MER RT flag, MER Tag Taylor series---MER QGH flag, MER QGQ flag, MER QGS flag, MER RT flag, MER Tag Series---MER QGH flag, MER QGQ flag, MER QGS flag, MER RT flag, MER Tag Series---MER QGH flag, MER QGQ flag, MER QGS flag, MER RT flag, MER Tag Series---MER QGH flag, MER QGQ flag, MER QGS flag, MER QGT flag, MER Tag Integrals that cycle, MER Tag Integration by parts, MER Tag Substitution---MER QGH flag, MER QGQ flag, MER QGS flag, MER RT flag, MER Tag Partial fractions---MER QGH flag, MER QGQ flag, MER QGS flag, MER RT flag, MER Tag Probability density function---MER QGH flag, MER QGQ flag, MER QGS flag, MER RT flag, MER Tag Probability density function---MER QGH flag, MER QGQ flag, MER QGS flag, MER RT flag, MER Tag Fundamental theorem of calculus---MER QGH flag, MER QGQ flag, MER QGS flag, MER RT flag, MER Tag Fundamental theorem of calculus---MER QGH flag, MER QGQ flag, MER QGS flag, MER RT flag, MER Tag Lagrange multipliers, MER Tag Optimization---MER QGH flag, MER QGQ flag, MER QGS flag, MER RT flag, MER Tag Lagrange multipliers---MER QGH flag, MER QGQ flag, MER QGS flag, MER RT flag, MER Tag Optimization---MER QGH flag, MER QGQ flag, MER QGS flag, MER RT flag, MER Tag Optimization---MER QGH flag, MER QGQ flag, MER QGS flag, MER RT flag, MER Tag Taylor series---MER QGH flag, MER QGQ flag, MER QGS flag, MER RT flag, MER Tag Sequences---MER QGH flag, MER QGQ flag, MER QGS flag, MER RT flag, MER Tag Differential equation---MER QGH flag, MER QGQ flag, MER QGS flag, MER RT flag, MER Tag Level curves---MER QGH flag, MER QGQ flag, MER QGS flag, MER RT flag, MER Tag Discrete probability---MER QGH flag, MER QGQ flag, MER QGS flag, MER RT flag, MER Tag Simpson's rule---MER QGH flag, MER QGQ flag, MER QGS flag, MER RT flag, MER Tag Riemann sum---MER QGH flag, MER QGQ flag, MER QGS flag, MER RT flag, MER Tag Trigonometric substitution---MER QGH flag, MER QGQ flag, MER QGS flag, MER RT flag, MER Tag Equation of a plane---MER QGH flag, MER QGQ flag, MER QGS flag, MER RT flag, MER Tag Equation of a plane---MER QGH flag, MER QGQ flag, MER QGS flag, MER RT flag, MER Tag level curves---MER QGH flag, MER QGQ flag, MER QGS flag, MER RT flag, MER Tag Trigonometric substitution---MER QGH flag, MER QGQ flag, MER QGS flag, MER QGT flag, MER Tag Riemann sum---MER QGH flag, MER QGQ flag, MER QGS flag, MER RT flag, MER Tag Fundamental theorem of calculus---MER QGH flag, MER QGQ flag, MER QGS flag, MER RT flag, MER Tag Fundamental theorem of calculus, MER Tag Substitution---MER QGH flag, MER QGQ flag, MER QGS flag, MER RT flag, MER Tag Integration by parts---MER QGH flag, MER QGQ flag, MER QGS flag, MER RT flag, MER Tag Taylor series---MER QGH flag, MER QGQ flag, MER QGS flag, MER QGT flag, MER Tag Simpson's rule---MER QGH flag, MER QGQ flag, MER QGS flag, MER QGT flag, MER Tag Taylor series---MER QGH flag, MER QGQ flag, MER QGS flag, MER QGT flag, MER Tag Probability density function, MER Tag Substitution---MER QGH flag, MER QGQ flag, MER QGS flag, MER RT flag, MER Tag Probability density function---MER QGH flag, MER QGQ flag, MER QGS flag, MER QGT flag, MER Tag Mean (continuous), MER Tag Probability density function---MER QGH flag, MER QGQ flag, MER QGS flag, MER RT flag, MER Tag Series---MER QGH flag, MER QGQ flag, MER QGS flag, MER RT flag, MER Tag Series---MER QGH flag, MER QGQ flag, MER QGS flag, MER QGT flag, MER Tag Integral comparison test, MER Tag Series, MER Tag Substitution---MER QGH flag, MER QGQ flag, MER QGS flag, MER QGT flag, MER Tag Differential equation, MER Tag Partial fractions---MER QGH flag, MER QGQ flag, MER QGS flag, MER QGT flag, MER Tag Fundamental theorem of calculus, MER Tag Integration by parts, MER Tag Substitution---MER QGH flag, MER QGQ flag, MER QGS flag, MER RT flag, MER Tag Multivariable calculus---MER QGH flag, MER QGQ flag, MER QGS flag, MER QGT flag, MER Tag Multivariable calculus---MER QGH flag, MER QGQ flag, MER QGS flag, MER QGT flag, MER Tag Optimization---MER QGH flag, MER QGQ flag, MER QGS flag, MER QGT flag, MER Tag Lagrange multipliers---MER QGH flag, MER QGQ flag, MER QGS flag, MER QGT flag, MER Tag Power series---MER QGH flag, MER QGQ flag, MER QGS flag, MER QGT flag, MER Tag Series---




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