Welcome to MATH 31A! This on-demand course was put together especially for MATH 31A at UCLA. Use the video lessons and notes to understand your lecture topics better, and the practice questions to cement your knowledge. And don't hesitate to leave a question in the Q&A box under each lesson if you need additional help with anything. Happy studying!
MATH 31A
UCLA
Course Overview
Lessons & Practice
I. Welcome
1. Pre-Calculus (Review)
3hr2. Limits
1.9hr2.15.1. One-sided Limits2.15.2. Limits2.15.3. Special Limits4 min2.15.4. Limits2.15.5. Limits2.15.6. Limits2.15.7. Limits2.15.8. Limits2.15.9. Limits2.15.10. Limits: Indeterminate forms2.15.11. Limits3 min2.15.12. IVT2.15.13. IVT2.15.14. IVT5 min2.15.15. Fundamental Trig Limit5 min2.15.16. Fundamental Trig Limit3 min2.15.17. Squeeze Theorem1 min2.15.18. Squeeze Theorem4 min2.15.19. Squeeze Theorem2.15.20. Continuity
3. Derivatives
2.8hr3.20.1. Derivative by Definition3.20.2. Basic Derivatives3.20.3. Basic Derivatives1 min3.20.4. Derivative by Definition3.20.5. Chain Rule3.20.6. Chain Rule3.20.7. Quotient Rule10 min3.20.8. Quotient Rule2 min3.20.9. Power of a Function Rule2 min3.20.10. Implicit Differentiation3.20.11. Implicit Differentiation3.20.12. Second Derivative6 min3.20.13. Logarithmic Differentiation4 min3.20.14. Logarithmic Differentiation 3.20.15. Inverse Trigonometric Derivatives3.20.16. Tangent Lines3.20.17. Tangent Lines3.20.18. Horizontal Tangent Lines2 min3.20.19. Product Rule6 min3.20.20. Product Rule4 min3.20.21. Product Rule4 min3.20.22. Normal Line5 min
4. Applications of Differentiation
4hr4.20.1. Related Rates4.20.2. Related Rates5 min4.20.3. Related Rates5 min4.20.4. Linear Approximation4 min4.20.5. Linear Approximation4.20.6. Taylor Series from Definition7 min4.20.7. Taylor Polynomials4.20.8. Maclaurin Polynomial4.20.9. Newton's Method2 min4.20.10. Newton's Method4.20.11. L'Hopital's Rule4.20.12. L'Hopital's Rule4.20.13. L'Hopital's Rule4.20.14. Limits4.20.15. L'Hopital's Rule4.20.16. L'Hopital's Rule4.20.17. Limits4.20.18. Limits4.20.19. Extreme Value Theorem4.20.20. Rolle's Theorem1 min4.20.21. Rolle's Theorem6 min4.20.22. MVT4.20.23. MVT2 min4.20.24. MVT3 min4.20.25. MVT4.20.26. Intervals of Increase and Decrease4.20.27. Intervals of Increase and Decrease3 min4.20.28. Critical Points6 min4.20.29. Critical Points1 min4.20.30. Extrema5 min4.20.31. Extrema6 min4.20.32. Second Derivative Test10 min4.20.33. Curve Sketching4.20.34. Curve Sketching12 min4.20.35. Curve Sketching4.20.36. Optimization4.20.37. Optimization4.20.38. Optimization
5. Applications of Differentiation for Science
41min6. Applications of Differentiation for Business & Econ
42min7. Differential Equations
1.2hr8. Integrals
2.7hr8.15.1. Antiderivatives: Indefinite Integrals8.15.2. Indefinite Integral with Trig and Inverse Trig8.15.3. Definite Integral with Trig1 min8.15.4. Integration by Substitution8.15.5. Integration by Substitution2 min8.15.6. Integration by Substitution3 min8.15.7. Integration by Substitution3 min8.15.8. Computing Integrals3 min8.15.9. Finite Sums3 min8.15.10. Finite Sums8.15.11. Finite Sums8.15.12. Riemann Sums8.15.13. Riemann Sums8.15.14. Riemann Sums8.15.15. Integral from Definition3 min8.15.16. Integral from Definition8.15.17. Definite Integral2 min8.15.18. Substitution with Definite Integral3 min8.15.19. Integration8.15.20. Definite Integral8.15.21. FTC I8.15.22. FTC I8.15.23. FTC I
9. Applications of Integration
1.8hr9.8.1. Displacement, Velocity, and Acceleration3 min9.8.2. Position, Velocity and Acceleration 2 min9.8.3. Position, Velocity and Acceleration 3 min9.8.4. Average Value of a Function2 min9.8.5. Average Value of a Function9.8.6. Average Function Value of a Function1 min9.8.7. Area Between Curves9.8.8. Area Between Curves4 min9.8.9. Area Between Curves9.8.10. Area Between Curves9.8.11. Volumes of Revolution, Cylindrical Shells9.8.12. Volumes of Revolution, Disc/Washer4 min9.8.13. Volumes of Revolution, Cylindrical Shells9.8.14. Volumes of Revolution9 min9.8.15. Arc Length4 min9.8.16. Arc Length4 min9.8.17. Arc Length with Partial Fractions7 min9.8.18. Arc Length with Perfect Square4 min9.8.19. Surface Area6 min9.8.20. Surface Area5 min
10. Applications of Integration for Physical Science
60min11. Integration Techniques
2.4hr11.10.1. Integration by Parts2 min11.10.2. Integration by Parts11.10.3. Integration by Parts11.10.4. Integration by Parts11.10.5. Integration by Parts11.10.6. Trigonometric Integral3 min11.10.7. Trigonometric Integral11.10.8. Trigonometric Integral with IBP5 min11.10.9. Trigonometric Substitution5 min11.10.10. Trigonometric Substitution6 min11.10.11. Trigonometric Substitution8 min11.10.12. Partial Fraction Decomposition8 min11.10.13. Partial Fraction Decomposition24 min11.10.14. Partial Fraction Decomposition4 min11.10.15. The Trapezoid Rule11.10.16. The Trapezoid Rule2 min11.10.17. Simpson's Rule
MATH 31A Overview
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Course Notes
Wizeprep's course notes with hundreds of easy-to-understand explanations, diagrams, and practice problems.
Course Notes
Wizeprep's course notes with hundreds of easy-to-understand explanations, diagrams, and practice problems.