MA1104: Multivariable Calculus
AY2012/2013, Semester 2, Lecturer: Loke Hung Yean
Course Coverage:
1. Vector-Valued Functions
2. Partial Derivatives
3. Gradients & Lagrange Multipliers
4. Double & Triple Integrals
5. Integrals in Vector Fields
6. Surfaces
7. Stoke's Theorem
8. Divergence Theorem
This module is the multivariate version of MA1102R. The module first introduces the vector-form of of function, and then generalizes the calculus results in its multivariate form.
The method of Lagrange multipliers is a common method used in constraint optimization where an objective function is optimized subjected to a given constraint. This method is widely applied in various fields ranging from physics and biology to economics.
Double and triple integrals are generalizations of the concept of integrals to surface and volumes. The focus in this course is more computational than analytical. Subsequently. these generalized results are applied to (dynamic) vector fields and surfaces.
The Stoke's Theorem is a vast generalization of the Fundamental Theorem of Calculus on manifolds, or in this module, surfaces. It states that the integral of a differential form of s over the boundary of some orientable manifold S is equal to the integral of the external derivative dS over the whole of S. On the other hand, The Divergence Theorem examines the flux of a vector field across an oriented surface in a particular direction. An appropriate (and overly-simplified) analogy liken the flux over a surface to the wind currents over the Earth's surface.
This module is conceptually and computationally difficult relative to its univariate version as it requires much more abstract thinking. Overall, this module is very relevant in applied mathematics, especially in engineering and the social sciences where, more often than not, there are more than one variables.
Workload: Heavy
Difficulty: Difficult
Grade: B-
Course Coverage:
1. Vector-Valued Functions
2. Partial Derivatives
3. Gradients & Lagrange Multipliers
4. Double & Triple Integrals
5. Integrals in Vector Fields
6. Surfaces
7. Stoke's Theorem
8. Divergence Theorem
This module is the multivariate version of MA1102R. The module first introduces the vector-form of of function, and then generalizes the calculus results in its multivariate form.
The method of Lagrange multipliers is a common method used in constraint optimization where an objective function is optimized subjected to a given constraint. This method is widely applied in various fields ranging from physics and biology to economics.
Double and triple integrals are generalizations of the concept of integrals to surface and volumes. The focus in this course is more computational than analytical. Subsequently. these generalized results are applied to (dynamic) vector fields and surfaces.
The Stoke's Theorem is a vast generalization of the Fundamental Theorem of Calculus on manifolds, or in this module, surfaces. It states that the integral of a differential form of s over the boundary of some orientable manifold S is equal to the integral of the external derivative dS over the whole of S. On the other hand, The Divergence Theorem examines the flux of a vector field across an oriented surface in a particular direction. An appropriate (and overly-simplified) analogy liken the flux over a surface to the wind currents over the Earth's surface.
This module is conceptually and computationally difficult relative to its univariate version as it requires much more abstract thinking. Overall, this module is very relevant in applied mathematics, especially in engineering and the social sciences where, more often than not, there are more than one variables.
Workload: Heavy
Difficulty: Difficult
Grade: B-