Welcome to MATH 5A! This on-demand course was put together especially for MATH 5A at UC Irvine. 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 5A
UC Irvine
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 Limits2.15.4. Limits2.15.5. Limits2.15.6. Limits2.15.7. Limits2.15.8. Limits2.15.9. Limits2.15.10. Limits: Indeterminate forms2.15.11. Limits2.15.12. IVT2.15.13. IVT2.15.14. IVT2.15.15. Fundamental Trig Limit2.15.16. Fundamental Trig Limit2.15.17. Squeeze Theorem2.15.18. Squeeze Theorem2.15.19. Squeeze Theorem2.15.20. Continuity
3. Derivatives
2.8hr3.20.1. Derivative by Definition3.20.2. Basic Derivatives3.20.3. Basic Derivatives3.20.4. Derivative by Definition3.20.5. Chain Rule3.20.6. Chain Rule3.20.7. Quotient Rule3.20.8. Quotient Rule3.20.9. Power of a Function Rule3.20.10. Implicit Differentiation3.20.11. Implicit Differentiation3.20.12. Second Derivative3.20.13. Logarithmic Differentiation3.20.14. Logarithmic Differentiation 3.20.15. Inverse Trigonometric Derivatives3.20.16. Tangent Lines3.20.17. Tangent Lines3.20.18. Horizontal Tangent Lines3.20.19. Product Rule3.20.20. Product Rule3.20.21. Product Rule3.20.22. Normal Line
4. Applications of Differentiation
4hr4.20.1. Related Rates4.20.2. Related Rates4.20.3. Related Rates4.20.4. Linear Approximation4.20.5. Linear Approximation4.20.6. Taylor Series from Definition4.20.7. Taylor Polynomials4.20.8. Maclaurin Polynomial4.20.9. Newton's Method4.20.10. 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 Theorem4.20.21. Rolle's Theorem4.20.22. MVT4.20.23. MVT4.20.24. MVT4.20.25. MVT4.20.26. Intervals of Increase and Decrease4.20.27. Intervals of Increase and Decrease4.20.28. Critical Points4.20.29. Critical Points4.20.30. Extrema4.20.31. Extrema4.20.32. Second Derivative Test4.20.33. Curve Sketching4.20.34. Curve Sketching4.20.35. 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 Trig8.15.4. Integration by Substitution8.15.5. Integration by Substitution8.15.6. Integration by Substitution8.15.7. Integration by Substitution8.15.8. Computing Integrals8.15.9. Finite Sums8.15.10. Finite Sums8.15.11. Finite Sums8.15.12. Riemann Sums8.15.13. Riemann Sums8.15.14. Riemann Sums8.15.15. Integral from Definition8.15.16. Integral from Definition8.15.17. Definite Integral8.15.18. Substitution with Definite Integral8.15.19. 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 Acceleration9.8.2. Position, Velocity and Acceleration 9.8.3. Position, Velocity and Acceleration 9.8.4. Average Value of a Function9.8.5. Average Value of a Function9.8.6. Average Function Value of a Function9.8.7. Area Between Curves9.8.8. Area Between Curves9.8.9. Area Between Curves9.8.10. Area Between Curves9.8.11. Volumes of Revolution, Cylindrical Shells9.8.12. Volumes of Revolution, Disc/Washer9.8.13. Volumes of Revolution, Cylindrical Shells9.8.14. Volumes of Revolution9.8.15. Arc Length9.8.16. Arc Length9.8.17. Arc Length with Partial Fractions9.8.18. Arc Length with Perfect Square9.8.19. Surface Area9.8.20. Surface Area
10. Applications of Integration for Physical Science
60min11. Integration Techniques
2.4hr11.10.1. Integration by Parts11.10.2. Integration by Parts11.10.3. Integration by Parts11.10.4. Integration by Parts11.10.5. Integration by Parts11.10.6. Trigonometric Integral11.10.7. Trigonometric Integral11.10.8. Trigonometric Integral with IBP11.10.9. Trigonometric Substitution11.10.10. Trigonometric Substitution11.10.11. Trigonometric Substitution11.10.12. Partial Fraction Decomposition11.10.13. Partial Fraction Decomposition11.10.14. Partial Fraction Decomposition11.10.15. The Trapezoid Rule11.10.16. The Trapezoid Rule11.10.17. Simpson's Rule
MATH 5A 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.