Pursuing a major in aerospace engineering is the first step toward a dynamic career designing and implementing aerospace machines, from military missiles to passenger planes. Essential to aerospace engineering undergraduate degree programs is adequate mathematical preparation, so Calculus I, Calculus II, Vector Calculus and Differential Equations are among a major’s required course list.

Calculus I

Calculus I is the first in the series of math courses required for aerospace engineering majors and should introduce you to the core concepts of single variable calculus. In addition to your understanding of the fundamental theorem of calculus, which establishes the fundamental link between a function, its integrals and its derivatives, you should learn to define and evaluate functions, limits, derivatives and integrals. You should also develop the ability to chart these elements graphically when applicable.

Calculus II

Your Calculus II course should continue expanding on the concepts introduced in Calculus I by explaining advanced applications of integrals and functions. Calculus II should, for example, relay how one deals with improper integrals as well as integral applications for volumes, or moments. You should also develop an understanding of inverse, exponential and logarithmic functions. Calculus II should also introduce the fundamental concepts of linear algebra, which is the core of multivariate calculus, explored more fully in Calculus III.

Calculus III or Vector Calculus

Vector Calculus, or Calculus III, should expose you to multivariate calculus, wherein you will learn about the extension of calculus into two and three dimensions. Accordingly, this level of calculus involves vector analysis, or the interpretation of an object or particle’s position, velocity and acceleration through three-dimensional space rather than as a singular along a line. Correspondingly you should learn about the calculation and application of partial derivatives, such as tangent planes or Lagrange multipliers, and multiple integrals. In addition, your Calculus III course should incorporate study of the central theorems of calculus, such as Green’s Theorem, or the two-dimensional extension of the Fundamental Theorem of Calculus that examines the relation between line integrals and double integrals to define a hypothetical plane.

Differential Equations

Some aerospace engineering programs also require you to take a course in Differential Equations, which complements your study of calculus by going into further depth on the theoretical underpinnings of the field while also extending calculus principles to the modeling of real world phenomena, such as population growth and decay or the depletion of natural resources. During this course you should master understanding of ordinary differential equations, or an equation containing a function of one independent variable and its derivative. You should also learn how to develop such models using first- and second-order differential equations while also being able to assess the impact on these models of different mathematical factors, such as undetermined coefficients or parameter variants.

#### References

- University of Tennessee Knoxville: Fundamental Theorem of Calculus
- University of Texas at Austin: 2012-2014 Aerospace Engineering Curriculum
- University of Maryland A. James Clark School of Engineering: Aerospace Engineering Four Year Academic Plan
- University of Michigan Ann Arbor School of Engineering: Aerospace Engineering Degree Requirements
- Carleton College Science Education For New Civic Engagements and Responsibilities: Ordinary Differential Equations in Real World Situations
- Lamar University: Definitions: Differential Equations

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