The San Diego Community College District's Accelerated College Program was established in 1963 by Dr. Robert Heilbron, President of Mesa College, in response to the need expressed by parents, advanced students, and high school administrators for academic work in political science and mathematics to augment the curriculum of the secondary schools. Today, the Accelerated College Program offers classes at 15 San Diego high schools taught by Mesa College faculty members. High school students may enroll in political science and/or calculus and earn up to 15 semester units of transferable college credit without leaving their high school campuses. Our enrollment of approximately 800 students provides evidence of the continuing need in our community for high quality college-credit courses provided by academic specialists to accelerated students in San Diego's high schools.

## Courses

## Student Learning Outcomes

- Evaluate various types of limits graphically, numerically, and algebraically, and analyze properties of functions applying limits including one-sided, two-sided, finite and infinite limits.
- Develop a rigorous limit proof for simple polynomials.
- Recognize and evaluate limits using the common limit theorems and properties.
- Analyze the behavior of algebraic and transcendental functions by applying common continuity theorems, and investigate the continuity of such functions at a point, on an open or closed interval.
- Calculate the derivative of a function using the limit definition.
- Calculuate the slope and the equation of the tangent line of a function at a given point.
- Calculate derivatives using common differentiation theorems.
- Calculate the derivative of a function implicitly.
- Solve applications using related rates of change.
- Apply differentials to make linear approximations and analyze propagated errors.
- Apply derivatives to graph functions by calculating the critical points, the points of non-differentiability, the points of inflection, the vertical tangents, cusps or corners, and the extrema of a function.
- Calculate where a function is increasing or decreasing, concave up or down by applying its first and second derivatives respectively, and apply the First and Second Derivative Tests to calculate and identify the function's relative extrema.
- Solve optimization problems using differentiation techniques.
- Recognize and apply Rolle's Theorem and the Mean-Value Theorem where appropriate.
- Apply Newton's method to find roots of functions.
- Analyze motion of a particle along a straight line.
- Calculate the anti-derivative of a wide class of functions, using substitution techniques when appropriate.
- Apply appropriate approximation techniques to find areas under a curve using summation notation.
- Calculate the definite integral using the limit of a Riemann sum and the Fundamental Theorem of Calculus and apply the Fundamental Theorem of Calculus to investigate a broad class of functions.
- Apply integration in a variety of application problems, including areas between curves, arc lengths of a single variable function and volumes.
- Estimate the value of a definite integral using standard numerical integration techniques which may include the Left-Endpoint Rule, the Right-Endpoint Rule, the Midpoint Rule, the Trapezoidal Rule, or Simpson's Rule.
- Calculate derivatives of inverse trigonometric functions, hyperbolic functions and inverse hyperbolic functions.
- Calculate integrals of hyperbolic functions and of functions whose anti-derivatives give inverse trigonometri and inverse hyperbolic functions.

- Solve first-order separable differential equations and initial value problems.
- Solve application problems involving first-order separable differential equations, such as exponential growth and decay.
- Solve integral problems by first examining the integral, then selecting and applying the appropriate technique of integration.
- Apply integration to physics problems relating to mass, centers of mass, work, and fluid force.
- Identify, analyze and evaluate improper integrals.
- Evaluate the limits of functions which have the indeterminate forms "zero/zero" and "infinity/infinity" using L'Hopital's Rule.
- Transform the other indeterminate forms into those which L'Hopital's Rule can be implemented.
- Define an infinite sequence; analyze and assess the monotonicity and convergence of a given sequence.
- Identify some basic series, including the geometric series, harmonic series and a telescoping sum.
- Compare the different convergence tests, including the Integral Test, the Ratio Test, the Root Test, the Comparison Test, the Limit Comparison Test, the Alternating Series Test, and the Divergence Test.
- Assess the convergence of a series by formulating the comparison of the given series to a known series.
- Assess if an alternating series converges absolutely, converges conditionally or diverges.
- Analyze a series, assess which convergence tests can be applied in determining its behavior, and apply this test to show the series convergence or divergence.
- Derive the Taylor series of a given function using a variety of techniques.
- Calculate the radius of convergence of a given power series.
- Apply Taylor's Theorem and Taylor polynomials to approximate to a certain degree of accuracy, the values of functions at non-trivial points.
- Apply the known power series expansions of important functions to generate the series expansion of other functions.
- Express a given second degree equation in the form of its standard conic equation and sketch the standard conic sections.
- Analyze a conic section by rotating it to a standard position.
- Sketch the graphs of functions in polar coordinates, including cardiods, lemniscates, and limacons.
- Calculate the areas of polar regions.
- Calculate the arclength of polar curves and the surface area bounded by polar curves.
- Calculate the equation of tangent lines to polar curves.
- Express a curve with parametric equations.
- Calculate the tangent lines and arclength of parametrized curves.

- Solve systems of linear equations using several algebraic methods.
- Construct and apply special matrices, such as symmetric, skew-symmetric, diagonal, upper triangular or lower triangular matrices.
- Perform a variety of algebraic matrix operations, including multiplication of matrices, transposes, and traces.
- Calculate the inverse of a matrix using various methods, and perform application problems involving the inverse.
- Compute the determinant of square matrices and use the determinant to determine invertibility.
- Derive and apply algebraic properties of determinants.
- Perform vector operations on vectors from Euclidean Vector Spaces including vectors from R^n.
- Compute the equations of lines and planes and write these in their corresponding vector forms.
- Perform linear transformations in Euclidean vector spaces, including basic linear operatons, and determine the standard matrix of the linear transformation.
- Prove whether a given structure is a vector space and determine whether a given subset of a vector space is itself a vector space.
- Determine if a set of vectors spans a space, and if such a set is linearly dependent or independent.
- Determine if a set of functions is linearly independent using various techniques including calculating the determinant of the Wronskian.
- Solve for the basis and the dimension of a vector space.
- Determine the rank, the nullity, the column space and the row space of a matrix.
- Describe orthogonality between vectors in an abstract vecotr space by means of an inner product, and compute the inner product between vectors of this inner product space.
- Compute the QR-decomposition of a matrix using the Gram-Schmidt process.
- Perform changes of bases for a vector space, including computation of the transition matrix and determining an orthonormal basis for the space.
- Compute all the eigenvalues of a square matrix, including any complex eigenvalues and determine their corresponding eigenvectors..
- Determine if a square matrix is diagonalizable and compute the diagonalization of a matrix whose eigenvalues are easily calculated.
- Perform linear transformations among abstract general vector spaces, determining the rank, the nullity and the associated matrix of the transformation.

## Transferability of College Credits

San Diego Mesa College is part of the State of California system of higher education. Accelerated College Program classes are sections of courses regularly taught at Mesa College. Therefore, credits earned in the Accelerated College Program are automatically (when transcripts are submitted) transferable to all California State Universities and all branches of the University of California. Each class carries a CAN (California Articulation Number) to assist universities in determining equivalencies. In addition, Accelerated College Program units are accepted by private colleges and universities in California (including Stanford and USC), and are accepted by most colleges and universities across the country, although some may impose various restrictions requiring petitions or placement tests. Receiving universities may allow the credits to be used for: subject requirements as a prerequisite for a major or related course, units toward a major, units toward graduation, GE requirements of the university(e.g. American institutions or quantitative reasoning), GE requirements of a college (e.g. depth and breadth for College of Arts and Letters), course equivalency. For example, at UCSD political science units earned in the Accelerated College Program satisfy the American Institutions requirement, transfer directly as political science units, and meet the requirements of the State of California for certification in certain professional programs. You should consult your college catalog or evaluator for policies in this area. Take the syllabus and course description provided by your ACP professor with you to orientation and registration session at your university.

## The Accelerated College Program and Advanced Placement (AP) Courses

Both Accelerated College Program and Advanced Placement (AP) courses allow students to take rigorous college level classes from excellent teachers on high school campuses. Advanced Placement courses are offered by the high school, so credits are used for the diploma; college credit depends on the results of the exam in May which the student may elect and pay to take. Accelerated College Program classes are provided through Mesa College, so no high school credit is given toward the diploma. Transferable college credits at Mesa College are earned by all successful students.

Students are selected for the Accelerated College Program by their high school counselors on the basis of previous grades, teacher recommendations and /or placement tests. Student learn from materials selected, prepared and present by their Accelerated College Program teachers, and are tested over those materials. Over 90% of our students pass and earn college credits.

## How does the Accelerated College Program affect San Diego High Schools

Each high school is allocated faculty positions (CPU's) by the San Diego Unified School District based on its student population, according to the District's formula, without consideration of our program. Our presence reduces the number of student who must be enrolled in high school classes. High schools can therefore reduce class size and/or assign released time for special purposes.

The high schools receive full ADA, provided Accelerated College Program students are enrolled in high school class four hours a day.According to the California Stat Department of Education, the Accelerated College Program enhances the high school curriculum by: 1) fostering articulation according to the State of California's Master Plan, and 2) enabling high schools to include college credit courses among the options for their students.