Differential calculus is concerned with finding the slope of a curve at different points. Integral calculus is concerned with finding the area under a curve.
Analysis is a broader term for Calculus and the theorems behind it. It is studied both with real and complex numbers as real and complex analysis. Usually calculus just deals with the basic problems of differential calculus and integral calculus.
You must have a strong basis in Algebra, Algebra II, Geometry and Trigonometry. Usually high schools offer a pre-Calculus course which is somewhat of a conglomeration of the aforementioned courses. Then you would move into differential calculus, integral calculus, vector (multi-variable) calculus, and finally differential equations, which is considered to be at the top of the hierarchy of the calculus courses. So take Algebra, Algebra II, Geometry and Trigonometry to get your strong foundation before begining the calculus sequence.
Liebniz and Newton
Once you've completed differential and integral calculus, multivariable calculus is often next step, and beyond that there is advanced calculus which generalizes calc to multidimensional spaces and uses vector-valued functions. Often concurrent with high level calculus in college courses is linear algebra and differential equations. There's nothing really 'after' calculus, because any topic in mathematics has a myriad of problems, theories, and potential applications to be explored. Calculus is, however, normally the highest level of math taught in US high schools and is a basic required course for any science/engineering major in college.
Just about all of calculus is based on differential and integral calculus, including Calculus 1! However, Calculus 1 is more likely to cover differential calculus, with integral calculus soon after. So there really isn't a right answer for this question.
John Philips Higman has written: 'A syllabus of the differential and integral calculus' -- subject(s): Calculus, Integral, Differential calculus, Integral Calculus
Alfred Lodge has written: 'Integral calculus for beginners' -- subject(s): Calculus, Integral, Integral Calculus 'Differential calculus for beginners' -- subject(s): Differential calculus
Differential calculus is concerned with finding the slope of a curve at different points. Integral calculus is concerned with finding the area under a curve.
Calculus, both differential and integral.
One directly undoes the process of the other.
G. Greenhill has written: 'Differential and integral calculus' -- subject(s): Calculus 'The third elliptic integral and the ellipsotomic problem' 'Gyroscopic theory'
People often divide Calculus into integral and differential calculus. In introductory calculus classes, differential calculus usually involves learning about derivatives, rates of change, max and min and optimization problems and many other topics that use differentiation. Integral calculus deals with antiderivatives or integrals. There are definite and indefinite integrals. These are used in calculating areas under or between curves. They are also used for volumes and length of curves and many other things that involve sums or integrals. There are thousands and thousand of applications of both integral and differential calculus.
T. G. Hall has written: 'A treatise on the differential and integral calculus' -- subject(s): Calculus
These are the general math courses in an undergraduate program of Mechanical Engineering. Actually, these are also the math courses required in ANY undergraduate Engineering curriculum: Algebra Trigonometry Analytic Geometry Differential Calculus Integral Calculus Mutivariable Calculus Differential Equations
Edward H. Courtenay has written: 'A treatise on the differential and integral calculus, and on the calculus of variations' -- subject(s): Accessible book, Calculus
L S. Hulbert has written: 'Differential and integral calculus'