# MATH1003

# Integral Calculus and Modelling

## [University of Sydney, Australia](/content/search?uniId=1/index.html)

### About course

This course looks at techniques of integration and their application to solve differential equations. The first part of the courses focuses on the derivation of integration using Riemann sums and then moves towards using integration to find area and volume as well as further techniques of integration. The second part of the courses uses many of these techniques of integration to solve differential equations which model natural phenomenon in the real world.

### About students

Coming soon!

### 1\. Introduction & Revision

|     |     |     |     |
| --- | --- | --- | --- |
| 1. | [MATH1003](/content/course/15/usyd/math1003/integral-calculus-and-modelling/video/1135/index.html) | FREE | 5:17 |
| 2. | [Revision - Differentiation Of Polynomials](/content/course/15/usyd/math1003/integral-calculus-and-modelling/video/1120/index.html) | FREE | 7:18 |
| 3. | [Revision - Integration Of Polynomials](/content/course/15/usyd/math1003/integral-calculus-and-modelling/video/1121/index.html) | FREE | 5:52 |
| 4. | [Revision - Differentiation And Integration Of Trig Functions](/content/course/15/usyd/math1003/integral-calculus-and-modelling/video/1122/index.html) | FREE | 7:20 |
| 5. | [Revision - Differentiation And Integration Of Exponentials](/content/course/15/usyd/math1003/integral-calculus-and-modelling/video/1123/index.html) | FREE | 7:52 |
| 6. | [Revision - Differentiation And Integration Of Natural Log](/content/course/15/usyd/math1003/integral-calculus-and-modelling/video/1124/index.html) | FREE | 8:21 |

### 2\. Riemann Sumes

### 3\. Definite & Indefinite Integral

### 4\. Area and Volume

### 5\. Integration by Substitution

### 6\. Integration by Parts & Reduction Formulas

### 7\. Logs, Exponential & Hyperbolic Functions

### 8\. Introduction to Ordinary Differential Equations

### 9\. Separable Equations & Trig/Hyperbolic Substitution

### 10\. Partial Fractions, Natural Growth & Logistic Function

### 11\. 1st Order Linear Differential Equations

### 12\. 2nd Order Linear Differential Equations

### 13\. Systems of Differential Equations

### 1.1 MATH1003

1.1 Introduction To Integral Calculus And Modelling from spoonfeedme on Vimeo

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