You CAN Ace Calculus
Single Variable Calculus
|Area Under Curves|
|Conics in Polar Form|
|Continuity & Discontinuities|
|Convolution, Laplace Transforms|
|Cylinder-Shell Method - Volume Integrals|
|Direct Comparison Test|
|Divergence (nth-Term) Test|
|Ellipses (Rectangular Conics)|
|Epsilon-Delta Limit Definition|
|First Derivative Test|
|Formal Limit Definition|
|Higher Order Derivatives|
|Hyperbolas (Rectangular Conics)|
|Infinite Series Table|
|Infinite Series Study Techniques|
|Infinite Series, Choosing a Test|
|Infinite Series Exam Preparation|
|Infinite Series Exam A|
|Initial Value Problems, Laplace Transforms|
|Integration by Partial Fractions|
|Integration By Parts|
|Integration By Substitution|
|Intermediate Value Theorem|
|Interval of Convergence|
|Inverse Function Derivatives|
|Inverse Hyperbolic Derivatives|
|Inverse Trig Derivatives|
|Limit Comparison Test|
|Moments, Center of Mass|
|Mean Value Theorem|
|Parabolas (Rectangular Conics)|
|Parabolas (Polar Conics)|
|Plane Regions, Describing|
|Radius of Convergence|
|Related Rates Areas|
|Related Rates Distances|
|Related Rates Volumes|
|Remainder & Error Bounds|
|Second Derivative Test|
|Slope and Tangent Lines|
|Arc Length (Vector Functions)|
|Arc Length Function|
|Arc Length Parameter|
|Conservative Vector Fields|
|Divergence (Vector Fields)|
|Double Integrals - Area & Volume|
|Double Integrals - Polar Coordinates|
|Double Integrals - Rectangular|
|Principal Unit Normal Vector|
|Triple Integrals - Cylindrical|
|Triple Integrals - Rectangular|
|Triple Integrals - Spherical|
|Boundary Value Problems|
|Classify Differential Equations|
|Existence and Uniqueness|
|First Order, Linear|
|Integrating Factors, Exact|
|Integrating Factors, Linear|
|Laplace Transforms, Solve Initial Value Problems|
|Linear, First Order|
|Linear, Second Order|
|Partial Differential Equations|
|Reduction of Order|
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Help Keep 17Calculus Free
So, you finished calculus 1. Congratulations! Do you think you are ready for calculus 2? Let's find out. Here are some practice problems from calculus 1 that use techniques that you need for calculus 2. Calculus 2 is the hardest of the three calculus courses and your calculus 1 skills need to be sharp. So here are some steps to help you determine if you are ready.
Here are the main topics you need for calculus 2.
1. basic limits
2. finite limits
3. infinite limits
1. basic power and trig rules
2. product rule
3. quotient rule
4. chain rule
5. maxima and minima
6. equations of tangent lines
1. basic integration
2. integration of basic trig functions
3. integration by substitution
4. area between curves
The chain rule is the single most important and most used rule of all of the derivative rules.
Integration by substitution is the single most important and most used rule of all the integration rules.
Here are the recommended steps to go through to make sure you are prepared for calculus 2.
1. If you struggled with algebra in calculus 1, which many students do, go to the precalculus section of 17university to review.
3. Make sure you are strong with the product rule, quotient rule and the chain rule. We don't mean just know what they are. We mean be able to do them in your sleep, almost without thinking and without looking them up in the textbook.
5. Once you are comfortable with the previous two steps, work some logarithmic differentiation problems. These will give you plenty of practice working with logarithms, which is the one topic almost all calculus students struggle with.
7. You need to know and really understand how to use integration by substitution. It is the one technique you will use in almost every integration problem you work. You need to be able to use this technique on both indefinite and definite integrals using correct notation.
8. You will be doing a lot of integration in calculus 2, so make sure you know how to integrate functions with exponentials, logarithms and basic trig functions.
9. It is important to know how to find the area under a curve since calculus 2 builds on that concept to find area between functions.
Okay, so if you have gone through all these steps and you feel confident, then you are well on your way to start calculus 2.