Calculus 1
University Study Guides
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. Integrals
2.7hr7.15.1. Antiderivatives: Indefinite Integrals7.15.2. Indefinite Integral with Trig and Inverse Trig7.15.3. Definite Integral with Trig7.15.4. Integration by Substitution7.15.5. Integration by Substitution7.15.6. Integration by Substitution7.15.7. Integration by Substitution7.15.8. Computing Integrals7.15.9. Finite Sums7.15.10. Finite Sums7.15.11. Finite Sums7.15.12. Riemann Sums7.15.13. Riemann Sums7.15.14. Riemann Sums7.15.15. Integral from Definition7.15.16. Integral from Definition7.15.17. Definite Integral7.15.18. Substitution with Definite Integral7.15.19. Integration7.15.20. Definite Integral7.15.21. FTC I7.15.22. FTC I7.15.23. FTC I
8. Applications of Integration
1.8hr8.8.1. Displacement, Velocity, and Acceleration8.8.2. Position, Velocity and Acceleration 8.8.3. Position, Velocity and Acceleration 8.8.4. Average Value of a Function8.8.5. Average Value of a Function8.8.6. Average Function Value of a Function8.8.7. Area Between Curves8.8.8. Area Between Curves8.8.9. Area Between Curves8.8.10. Area Between Curves8.8.11. Volumes of Revolution, Cylindrical Shells8.8.12. Volumes of Revolution, Disc/Washer8.8.13. Volumes of Revolution, Cylindrical Shells8.8.14. Volumes of Revolution8.8.15. Arc Length8.8.16. Arc Length8.8.17. Arc Length with Partial Fractions8.8.18. Arc Length with Perfect Square8.8.19. Surface Area8.8.20. Surface Area
9. Applications of Integration for Physical Science
60min10. Integration Techniques
2.4hr10.10.1. Integration by Parts10.10.2. Integration by Parts10.10.3. Integration by Parts10.10.4. Integration by Parts10.10.5. Integration by Parts10.10.6. Trigonometric Integral10.10.7. Trigonometric Integral10.10.8. Trigonometric Integral with IBP10.10.9. Trigonometric Substitution10.10.10. Trigonometric Substitution10.10.11. Trigonometric Substitution10.10.12. Partial Fraction Decomposition10.10.13. Partial Fraction Decomposition10.10.14. Partial Fraction Decomposition10.10.15. The Trapezoid Rule10.10.16. The Trapezoid Rule10.10.17. Simpson's Rule
11. Additional Resources
12. Differential Equations
1.2hrI Welcome
Free Activity
Welcome to Calculus!
My name is Corey and I'm the instructor for this course. Feel free to go through this course at your own pace.
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Happy Studying!
Answered
Anonymous
What are the conecpts to focus on for midterm 1 at western
C
Corey M
InstructorLikely limits and differentiation techniques through the chain rule, but double-check with your instructor to see exactly what will be covered.
Unanswered
L
Layan E
Use the Intermediate Value Theorem to show that thereis a root of the given equation in the specified interval.Use the Intermediate Value Theorem to show that thereis a root of the given equation in the specified interval.
sin(x)=x2−x, x∈(1,2)
C
Corey M
InstructorWhile this isn't quite the place for this question (please refer to the IVT section in the course), and we can't really just solve random problems for you, I can give you a bit of a hint: You could try moving everything to one side of the equation and treating it like a function, and then see if you can't find function values within your specified range that return a positive value and a negative value (another hint: try the endpoints of your interval first). If you're able to do that, then the IVT tells us that there should exist a function input between those two points that returns 0 or, in other words, that is a root.