__Calculus 2__

__Calculus 2__

#### The Calculus 2 online course starts by building key integration techniques before exploring their applications. Students then move on to learn parametric & polar functions, and sequences & series. Calculus 2 is a key course for students pursuing Math, science, technology or engineering. Check out the classroom with the previews or start FREE one week trial.

__Calculus 2 Curriculum__

__Calculus 2 Curriculum__

- Antiderivatives (7:42)
- Antiderivatives and Integration (10:10)
- Notation for Integration (12:19)
- The Power Rule (14:39)
- Integratable Form (10:40)
- Indefinite and Definite Integrals (6:46)
- Evaluating Definite Integrals (13:33)
- Riemann Sums (9:52)
- Integrals and Riemann Sums (7:42)
- The Fundamental Theorem of Calculus (13:01)
- Practice Questions

- Integration by U-Substitution (18:09)
- The Reverse Chain Rule (11:06)
- Integration by Parts (17:59)
- Integration by Parts for Definite Integrals (14:49)
- Integration using Partial Fractions (35:20)
- Integrating the Sine and Cosine Functions (8:46)
- Integrating the Tangent Function (7:49)
- Integrals Involving Exponential and Logarithmic Functions (11:17)
- Improper Integrals (16:29)
- Evaluating Improper Integrals of the Form [a, infinity) (11:33)
- Evaluating Improper Integrals of the Form (- infinity, infinity) (13:46)
- Evaluating Improper Integrals - Discontinuous at ‘a’ or ‘b’ (10:47)
- Improper Integrals – Discontinuous in the interval (a, b) (14:50)
- Practice Questions

- Finding the Area Under a Curve (16:51)
- Finding the Area Between Two Curves (18:59)
- Volumes of Revolution (9:53)
- Volumes of Revolution Around the X-Axis (11:57)
- Volumes of Revolution Around the Y-Axis (16:44)
- Arc Length Using Integration (9:09)
- Evaluating Arc Length Using Integration (19:56)
- Practice Questions

- Parametric Functions (10:14)
- Writing Parametric Functions in Cartesian Form (15:38)
- Differentiating Parametric Functions (13:26)
- Second Derivatives for Parametric Functions (15:30)
- Curves of Parametric Functions (15:52)
- Tangent Lines to Parametric Curves (17:46)
- The Area Under a Parametric Curve (13:42)
- The Arc Length of a Parametric Curve (29:52)
- Volumes of Revolution for Parametric Curves (13:33)
- Surface Area of Revolution for Parametric Curves (11:50)
- Practice Questions

- Polar Co-ordinates (8:35)
- Switching Between Polar and Cartesian Co-ordinates (16:34)
- Graph Sketching for Polar Curves (32:38)
- Tangent Lines to Polar Curves (28:12)
- The Intersection of Polar Curves (20:36)
- The Area Bounded by a Polar Curve (14:43)
- The Arc Length of a Polar Curve (18:48)
- The Surface Area of Revolution of a Polar Curve (16:07)
- Practice Questions

- Partial Sums of an Infinite Series (11:51)
- Sum of an Infinite Series Using Partial Sums (22:26)
- Geometric Series Convergence Test (16:15)
- The Sum of a Geometric Series (16:12)
- Repeating Decimal Problems (7:52)
- Telescoping Series (26:17)
- The Sum of a Convergent Telescoping Series (11:34)
- The Limit and Sum of an Infinite Series (9:28)
- Common Series Results (12:50)
- Practice Questions

- The Integral Convergence Test (17:56)
- The P-Series Test (12:45)
- The Nth Term Test (16:19)
- The Direct Comparison Test (14:19)
- The Limit Comparison Test (15:44)
- The Ratio Test (17:49)
- The Root Test (17:20)
- Absolute and Conditional Convergence (17:19)
- Alternating Series Test (20:20)
- Alternating Series Estimates (12:30)
- Practice Questions

- Starting Power Series (7:18)
- Power Series, Taylor Series and Maclaurin Series (9:49)
- Radius and Interval of Convergence (10:18)
- Multiplying Power Series (14:51)
- Differentiating Power Series (7:43)
- Evaluating Indefinite Integrals for Power Series (10:52)
- Evaluating Definite Integrals for Power Series (10:34)
- Starting Maclaurin Series (16:59)
- Evaluating the Sum of a Maclaurin Series (8:32)
- The Radius and Interval of Convergence of a Maclaurin Series (26:22)
- Writing Indefinite Integrals as an Infinite Series (8:31)
- Approximating Definite Integrals Using an Infinite Series (24:02)
- Starting Taylor Series (13:52)
- The Radius and Interval of Convergence of a Taylor Series (24:33)
- Practice Questions

**Who is the Calculus 2 Course For?**

Calculus 2 is for students who have experience of Differential Calculus and want to develop similar Integral Calculus skills. Students taking Calculus 2 should have ideally completed a course in Calculus 1. View the CLASSROOM.

**What is Taught in Calculus 2?**

Core and Advanced Integration Techniques, Applications of Integrals, Parametric & Polar Functions, Sequences & Series, Series Convergence Tests, Power Series. View the full CURRICULUM.

**What Will I Take Away From This Course?**

Students will master various Integration techniques & applications, and will gain considerable experience of sequences & series. Students practice what they’ve learnt from our instructional videos using carefully designed Calculus 2 worksheets.

**How Does Calculus 2 Compare to Calculus 1?**

Calculus comes in two flavours. Calculus 2 focuses on Integral Calculus and Calculus 1 focuses on Differential Calculus.

**What is the Progression From Calculus 2?**

Students are in a strong position to take Vector Calculus, Mathematical Analysis or to apply Calculus in real-world scenarios.

#### Hi, I’m Gary, and I'll be your instructor for this course in Calculus 2.

I'll be straight with you, I love Math! But I completely get that for most of us it's very challenging, and often frustrating. I'm here to help make it easier for you. I've taught many Calculus 2 students. I understand the sticking points and how to help you develop skills and boost your confidence. I have a BSc Honours degree in Pure Mathematics and have been educated in both the UK and the US. I own and run a private tuition business where I've served many hundreds of Maths students.